The Dash Mahavidyas are an enigmatic group of goddesses worshiped majorly in the Tantrik disciplines but except Kali, the origins of most are unclear. In which scriptures can we find more about the other nine Mahavidyas?
First of all it's a very very long answer.
PurAnic accounts of how the DashamahAvidyAs manifested
The following account appears in Devi PurAna, however the same appears also in the BhAgavata PurAna (as per some book that i have):
Once the greatest of Yogis, Lord Maheswara worshiped MahAdevi and obtained from her the boon that She will be his wife. Lord Brahma upon realizing that soon MahAdevi will manifest herself as per the boon, orders one of his favorite sons, Daksha, to engage in penance so that the would be consort of Lord Shiva can be his daughter.
Daksha thus did a severe tapasyA to MahAdevi and she appeared before him. When asked what boon does he want, Daksha said he wants MahAdevi to be born as his daughter. MahAdevi granted that boon and said when she will descend to be the wife of Lord Shiva she will take birth from Daksha's wife Prasuti's womb. But she also reminded him that once Daksha's merits end or if he somehow disreagrds her, she will leave him instantly.
The Daksha Yajna episode is well-known so i am not repeating it in full here. When, Lord Shiva saw that Sati was adamant to attend his father's Yajna inspite of his disapproval got a little angry and reprimanded her saying:
Janami vagvahirbhutAm tvAmaham dakshakanyake |
yatharuchi kuru tvancha mamajyAm ki pratikshase ||
I know that you are not bound by my orders, so do as you please, why are you waiting for my consent?
Upon hearing Shiva's strong words Devi got angry. And thought to hersef that Shiva, upon obtaining her as his wife, forgot her real form (which is of Parama Shakti). So let me abandon him and my proud father and stay in my own swarupa and in my own lila for sometime.
tyaktanamapi darpishtham pitarncha prajApatim |
SamsthAsyAmi kiyatkAlam swasthAnam nijalilAyA ||
On thinking thus, Devi assumed the terrible form of MahAkAli. Which was of a Goddess who is dark complexioned, digamabari (without clothes), lolajihvA (tongue hanging out and clasped with the teeth), with disheveled hair and wearing garland comprised of slain heads.
Lord Shiva was terrified on seeing Goddess's such terrible form and tried to escape from that place immediately.
Upon seeing her terrified consort Shiva, Devi, out of mercy and in order to block all the ten directions (so that Shiva can not escape through any one of them), assumed ten different forms with each blocking one direction.
Evam patim vikshya bhayAbhibhutakam dayAnvitA tat prati vAranecchayA |
sarvAsu dikshu kshanamAtramadhyataha stithA cha bhutvA dashamurtayastadA |
Whichever directions Lord Shiva tries to escape through, finds one or the other terrible forms of Devi guarding there. So, unable to find an way to escape Lord Shiva closed his eyes out of fear and upon opening them again found the terrible Goddess MahAkAli right in front of him.
Lord Shiva asked " Who are you ShyAmA (the dark complexioned one)? Where is my beloved Sati?"
Devi laughingly replied " Can't you recognize me? Iam your own Sati. Im the SrishtistithisamhArakArini SukshmA Parkriti. For being your wife i have become fair complexioned (Gauri). The ten Devis that you see around you are also my forms. Hence, O MahAmati Shambhu, do not fear:
Sati said to her husband who was afflicted with fear " The Goddess who is in your front is BhimanayanA MahakAli, in the sky (or in the antariksha direction) is TArA, on the right side is ChinnamastA, on your left is Bhuvaneswari, behind you is BagalAmukhi, at the south-east corner (Agni Kona) is DhumAvati, in the south-west corner (Nairitkona) there is KamalA, in the north0west corner (VAyukona) there is MAtangi , in the north-east corner (IshAna kona) there is Shodashi (Tripura Sundari) and in your own self i am existing as Bhairavi.
Now, if you want i can teach that proud Daksha a lesson by destroying his Yajna.
A different account is given in the Devi BhAgavatam and which is as follows:
In ancient times, in the lineage of Hiranyaksha was born as the son of Asura Ruru, a valorous, powerful and extremely cruel Asura called Durgama. Once he thought within himself " Since Vedas are the real force sustaining the Gods, if Vedas themselves can be destroyed the Gods can be made extict as well." Thinking like this he goes to Himalayas and statred meditating upon Lord Brahma in his penance.
Only feeding on air, Durgama did an extreme penanace which lasted for 1000 years.Eventually Lord Brahma appeared before him , and pleased with his penance told him to ask for a boon. The boon that Durgama asked was like this " Hey Lord give me the charity of all the Vedas. Give such boon by power of which may all the Veda mantras, that used to hitherto exist in the hearts of the Dvijas of the three worlds, should from now on be present only in me. That's how i may defeat the Devas"
Lord Brahma granted that boon and disappeared. (Devi BhAgavatam 7.28-12,14) ( pujayitvA varam vavre vedAn dehi sureswara .... jagAm satyalokantu chaturvedaswarah parah ).
Immediately afterwards, as the boon started taking effect, all the Vipras forgot the Veda mantras. All the Vedic rituals, as a result, ceased. Deprived of the fire-oblations that used to be poured in Yajnas the Gods gradually became weak. Taking advantage of the situation, Durgama with his troops took control of Amaravati and the Gods were forced to leave their own place. The Gods went to Sumeru's caves and fort made of rocky mountains and took shelter in them. They started meditating upon MahAshakti. During the same time, the earth was also facing severe lack of rains for some 100 years and there was draught and deaths all round as a result.
The high-souled Brahmins hence went to the sides of the Himalayan range and started praying to Bhagavati ShivAni . They did the peanance without food intake and prayed to Goodess:
Namah kutastharupAyai chidrupAyai namo namaha|
Namo vedAntavedyAyai bhuvaneshyai namo namaha ||.
As a result of that penance, Goddess was pleased and Devi Bhuvaneswari, Maheswari, PArvati displayed her spectacular form which is endowed with infinite number of eyes.
Iti samprArtitA devi bhuvaneshi maheswari |
anantAkshimayam rupam darshyAmAs pArvati || (Devi BhAgavatam 7.28.31-33)
From those infinite number of eyes of Goddess PArvati, for nine days, continuously flowed tears.And as a result the dry and lifeless earth got rejuvenated. The Gods came out of the caves and started eulogizing Goddess. Durgama got informed of all the happenings from spies and came to fight Goddess.
Now, during this battle from Goddess SatAkshi's body emerged 32 MahAshaktis and 64 Divyashaktis and numerous Shaktis all equiped with many weapons. Among the 32 MahAshati we find the names of all the MahAvidyas except DhumAvati and Buvaneswari.
KAlikA tArini bAlA tripurA bhairvai ramA|
bagalA chaiva mAtangi tathA tripurAsundari ||
KAmAkshi kulajA devi jambhini mohini tathA |
ChinnamastA guhyakAli dashasAhasra bahukA ||
DvAtrimshacchayashchAnyA devyah samudbhutAstu sAyudhAh || (Devi BhAgavatam 7.28.55-57)
To be noted here, that except Bhuvaneswari and DhumAvati, all MahAvidyas are mentioned. But the word MahAvidyA is not used explicitly. Also names of other well-known Goddesses (like KAmAkshi) are also mentioned along with.
The names of the 10 MahAvidyas are also mentioned in the upapurAna Brihaddharma:
MahAvidyA imAh proktA nAmAnyAsantu varnaye |
KAli tArA mahAvidyA shodashi bhuvaneswari ||
BhairvaichinnamstA cha sundari bagalamukhi dhumAvati cha mAtangi mahAvidyA dashaiva TAh || (Brihaddharma PurAna, MadhyabhAga).
Here ends the PurAnic accounts of the MahAvidyAs.
Respective origins of MahAvidyAs from Tantras:
I could not find any story for Bhairavi and Bhuvaneswari (who is of course Goddess PArvati's ShatAkshee form). Also, for MahAkAli i could not find any story either probably because she is AdyA or the primordial.
One such story is found in the Swatantra Tantram and another one in the NArada PanchrAtra. The later story is also quoted in PrAnatoshini Tantra's 5th KAnda's 6th chapter. I am only giving this version. Although i know the other story but i am not posting it here.
EkadA pArvati devi snAnArtham gatavatyapi
....... Evam kritvA tu tAstatra gatAh sarvA yathAgatam |
Chinnam tasyA yato mundam chinnamastA tatah smritAh ||
One day Goddess PArvati went, along with her two Sakhis, DAkini and Varnini, to MandAkini to bath. After bathing the two sakhis felt hungry and pleaded Devi for food. Devi asked them to wait for sometime. After few moments has elapsed the sakhis pleaded again by saying " Give us food". They further said- "You are the mother of the whole world. And a child always asks from its mother. That's why we are asking from you for something to eat" Devi replied, that she will arrange for food once they reach home. But DAkini and Varnini, afflicted with hunger, pleaded again saying " Hey Mother of the world, we are hungry, please give us some food which satiates our hunger. ,Upon hearing such words Devi immediately severed her own head with the tip of nails of her left hand. The severed head fell on Devi's left hand. Out of the severed head, three streams of blood gushed out. Of which the stream that went towards left was drunk by DAkini, the stream that went to right fed Varnini and Devi herself drank the middle stream. All these events happened without anyone's notice. After that, Devi along with her sakhis returned home. Since Devi's head was severed she came to be known as ChinnamastA.
Atha vakshyAmi deveshi bagalotpattikaranam |
PurA kritayuge vAtakshobha upastithe ||
.... BrahmAstravidyA samjAtA trailokya stambhini parA..
[Lord Shiva says to Devi] In ancient times, during Krita Yuga (or Satya Yuga) there was a time when wind flowed on earth at great speed. Lord Vishnu started worrying that this powerful wind-flow might destroy the whole world. And he began to do a severe Tapasya (penance) to discover a remedy. Pleased by Vishnu's severe penance, which went on for 1000 years, Goddess MahAtripurA Devi stopped that wind flow. Thereafter the Great Goddess saw a big lake called Haridra and started playing in it. And after that, in a nearby place called Saurashtra, an resplendent Goddess emerged from that yellow lake at midnight of Krishna Paksha Chaturdasi ( 14th day of the dark phase of moon) and the day was Tuesday. In Tantra Texts this great night is known by the name of VirarAtri. And this Goddess is the eighth SiddhavidyA called BagalAmbikA.
From Swatantra Tantram.
Could not find the complete story. Goddess TarA is also known as Nila Saraswati. The story given below records why she is associated with the blue color:
Mere pashchimakule tu cholanAkhyA hrado mahAn |
Tatra yajne swayam devi nilasaraswati ||
Tatra japantu prajapamstriyugam samavartata |
On the west side of Meru there's a lake called Cholana. From this lake arrived Goddess Nilasaraswati or TArA. On the banks of this lake Goddess did japa for three Yugas. beams of light rays fell on the lake from her higher face ( mahordhavaktaro nihsrito tejorAshivinirgato- don't know how to translate this better) and that's how Goddess obtained blue color
Daksha prajapateryajne sarvasamhAra chanchala |
KruddhA deham vinikshepya tato dhumohabhavanmAhAn ||
TasmAddhumAvati jAtA sarvashatruvinAshini.
Goddess Sati, terribly enraged and in a mood to destroy all, threw herself into the fire-pit of the Yajna which was arranged by Daksha PrajApati. Consequently, a whole lot of smoke appeared of the fire-pit. Out of that smoke Goddess DhumAvati appeared, who is the destroyer of all enemies.
The NArda Pancha RAtra gives another story and which which is like this:
Once in KailAsha Goddess Girija told to Lord Shiva "I am hungry give me something to eat". Lord Shiva asked her to wait for some while. After some moments have elapsed, Goddess again asked for food from Shiva. Shiva replied " Please wait for some more time". Goddess got impatient and said to Lord Shiva " Hey Lord of the universe, give me some thing to eat, i can't tolerate any more delay". Saying thus, she devoured Shiva himself. Then within moments her body began emitting a whole lot of smoke. Out of his own mAyA Lord Shiva obtained another body and said to Goddess " Hey Devi, see with your jyAnachakshu (the inner eyes) , there isn't any male other than me ( in the whole world) neither a female except you. Today you have devoured your own husband and thus you have become a widow. So, hey Oh devoted Wife, abandon all signs of a married woman. Your this supreme murti will be famous as BagalAmukhi and since your body was enwrapped with smoke (dhuma) you will also be known as DhumAvati.
So, note that according to this story BagalAmukhi and DhumAvati are just the same.
Atha mAtanginim vakshye krurabhuta- bhayankarim
... TejorAshirbhuttatra swayam srikAlikAmbikA |
ShyAmalam rupamAsthAya rAjamAtangaini bhavet ||
In ancient times,in a garden of kadamba flowers which was filled with various trees, Matanga Muni once did tapasyA for obtaining full control over all beings (Vashikarana) for hundreds of thousands of years ( satavarshasahasrAni in original text). as a result of that penanace Goddess Sunadri's eyes emitted light-energy (teja). That tejarAshi thereafter assumed the form of Mother KAlikAmbikA. And that form assumed dark complexion and became the dark-colored RAjamAtangi.
PurA brahmA jagatsrashtum tapohatapyat dArunam |
..... JAtA tasyAm mahAlakshmih sarva saubhAgya dAyini ||
In ancient times, Lord BrahmA, for the purpose of creation, performed a severe penace. Parameswari TArini (or TArA) pleased with that penace herself appeared on the day of Chaitra ShuklA Navami.She has appeared before too during the event of the churning of the ocean. She is RamA , the one who sits on a lotus-throne and the one who is situated in the heart of Vishnu. In BhAdrapada month's KrishnAshtami Tithi her MahAmatangi form appeared, who is known as the destroyer of KolAsrua. In phAlguna month's tuesday or friday giver of all the fortunes, MahAlakshmi was born.
From NArada PancharAtra :
Once the apsaras from heaven went to see MahAdeva in KailAsha. Lord Shiva , in front of them, called Devi by taking the name "KAli KAli". Devi felt ashamed and offended and decided that she will get rid of her KAli swarupa and will change it to Gauri swarupa (or the fair-complexioned one). With this resolve Devi disappeared from KailAsha. Lord Shiva was as a result left alone. During one such days NArada vistted KailAsha. He asked Lord Shiva about Devi. Shiva said that she has left him and disappered from KailAsha. NArada meditated and found out that Devi's location at that point of time was northern side of the Sumeru mountains. NArada immediately went there and started eulogizing Devi with stava-stutis. Devi was pleased thereby and asked NArada about the whereabouts of Lord Shiva. Narada said " O Mother, Maheswara is all geared up for another (the 2nd) marriage. Please come over there and stop the marrige." Devi returned to KailAsha upon assuming an extremely beautiful appearance, which is unparalled in the three worlds. Devi neared Shiva and found her own image in Shiva's heart. But, thinking that the image is of some one else, she started reprimanding Shiva accusing him to be ungrateful and breaker of vow. Shiva then said " Devi, meditate, and see with your inner eyes (jyAna drishti) , the shadow or image in my heart is of you only". Devi did likwise and calmed down upon finding what Lord Shiva said is right. When Devi asked about the mystery of the shadow (chAyA) in the heart, Shiva said in that context:
YasmAt tribhuvane rupam sreshtham kritavati shive |
TasmAt swarge marte cha pAtAlehanyatra pArvati ||
SUndari panchami sri cha khyAtA tripurasundari |
SadA shodasha varshiyA vikhyAtA shodashi tatah ||
Since you have assumed the most beautiful appearence in the three worlds, you will be known in swarga, martya , pAtAla and everywhere else, as Sundari, Panchami, Sri and Tripurasundari. And since you are always sixteen year old, you are famous as Shodashi.
But note that there more reasons why Goddess have the names- Tripura and Shodashi.
In which scriptures can we find more about the other nine Mahavidyas?
You can find them in the Agamas. Few of the names of such Agamas are already mentioned in my answer. Few others like KAlikula sarvasya, ViswasAra Tantram, TArA Rahsya, ShyAma Rahasya, Todala Tantram, MahAvidyA Tantram and amny others.
Anyways, i am providing a bit more info on the DashAmahAvidyas here:
RAtri- The days on which the MahAvidyAs appeared
The arrival Tithis are given in Tantras and there they have the name RAtri. This is a Tantrik terminology. For different Deities a different RAtri. Also, just like RAtri is the name of the arrival Tithi it is the name of the Goddess also. For example, Goddess MahAkAli's one name is MahArAtri and her arrival Tithi is also known as MahAratri. Similarly Goddess TArA's one name is KrodharAtri and one of her names is also the same. For the remaing Devis arrival Tithis are:
We know what those days are from Swatantra Tantram as follows:
PhAlgune cha mahArAtrih krishnaikadashika tithih|
........ Chaturdashi bhaumayuktA makArena samanvitA |
KulasmarismAyuktA virarAtri prakirtitA ||
MahArAtri- Phalguna month, Krishna Paksha, EkAdashi Tithi.
DivyarAtri- Jaishtha month, SuklA Dashami if falls on Friday.
TArArAtri- Tuesday, AmavasyA, Sun SamkrAnti, and with Kula nakshtara ( Nakstras, Days, Tithis etc are classified into Kula, Akula and KulAkula categories in Agamas, with Kula as being related to Goddess is considered as the most auspicious)
SiddharAtri- Chaitra SamkrAnti if falls on Ashtami Tithi.
DArnurAtri- Vaishakha month, SuklA TritiyA, with Kula Nakshtra.
KAlArAtri- DipAnvita Chaturdashi and AmAvasyA.
VirarAtri- Magha month, Tuesday, Chaturdashi Tithi and with Kula Nakshtra
Among these the KAlArAtri is extremely dear to KAli and TArA. viz-
KAlarAtrimaheshAni tArAAkAli priyankari.
Bhairava- The consorts of the MahAvidyAs
As we know that the relation between Shiva-Shakti is that of inseparability So, each MahAvidyA also has one aspect of Shiva as her consort. They are called the Bhairavas in Tantra.
As per Shaktisamgama tantram the Bhiarava's names are as follows:
KAlikAyA mahAkAlah sundaryA laliteswarah....
Mrityunjayastu bagalAvidyAyAh parikirtitah||
KalikA's Bhairva- MahAkAla,
and BagalA's Bhairava is Mrityunjaya.
However as per Todala Tantram the Bhairvas are different.
Tripura Sundari- Panchavaktra (five-faced) Shiva,
chinnamastA- Kavandha Shiva,
DhumAvati does not have a consort as she is widow,
BagalAmukhi- Ekvaktra MahArudra,
KamalA- Vishnurupa SadAshiva.
(KamalAyA dakshinAmshe vishnurupam sadAshivam)
How many MahAvidyAs- 10 or more?
Although 10 is famous. But different opinions in scriptures are also there.
Within the major Tantric scripture called Vishnu KrAnta many other scriptures exist. One among them is aclled MundmAla Tantram. Till date, two manuscripts of mundamAla has been found. The first manuscript gives the famous 10 names:
KAli tArA mahAvidyA shodashi bhuvaneswari |
Bhairavi chinnamstA cha vidyA dhumAvati tathA ||
BagalAmukhi siddhavidyA mAtangi kamalAtmikA |
EtA dasha mahAvidyA siddhavidyA prakirtitAh ||
The 2nd manuscript gives the following names:
YathA kAli tatha tArA tathA tripurasundari |
Bhairavi bhuvana vidyA chinnA cha bagalAmukhi ||
DhumAvati chAnnapurnA durgA cha kamalAtmikA |
MAtangi dhanadA padmAvati sarvArtha siddhidA ||
MundamAlA Tantram 1.14-15.
So, we find some more names here viz- DurgA, AnnapurnA, DhanadA and PadmAvati. Also, note that, as per RAdhA Tantram, Goddess TripurA's emissary PadmAvati is the one who incarnates as the physical RAdhA.
Apart from the usual 10, the Niruttara Tantram, also mentions more Deities among MahAvidyAs viz- DurgA, JayadurgA, AnnapurnA, Sarswati, TwaritA, BhadrA, TripurA and Mahishamardini.
The MAlinivijaya Tantram gives the following names:
KAli niilA mahAdurgA twaritA chinnamastakA |
VAgvAdini chAnnapurnA tathA pratyAngirA punah ||
KAmAkhyAvAsini bAlA mAtangi shailavasini |
Iti AdyAh sakala vidyAh kalau purnaphalapradAh ||
So the new names are- MahAdurgA, TwaritA, Saraswati, AnnapurnA, PratyAngirA, KAmAkhyAvAsini and ShailavAsini (or Mahishamradini). In the above verses Goddess TArA has been mentioned as NilA and Goddess Bhairavi as BAlA. The last verse says- All of them are MahAvidyAs, fully functional in Kali Yuga and AdyAswarupa.
In Shaktisamgama Tantram 6.16-17 the same 10 mAhavidyas (mahAvidyA dashiava tu) are mentioned but at some other place it also mentions about 13 MahAvidyAs viz- Tarayodasha mahAvidyA virupAkshena kirtitA.
According to NirvAna Tantram (also part of VishnukrAntA) the mahAvidyAs are 8 in number.
MahAvidya KAli's mind born son is Lord BrahmA. Upon his request, MahAkali created from herself the 2nd MahAvidyA Savitri. And following MahAkAli's orders the duo got engaged in the process of creation. Upon 2nd mind born son- Vishnu's request MahAkAli created from within herself the 3rd MahAvidyA, Sri. And thereafter, the duo (Vishnu-Sri) got engaged in the task of preservation. Upon the 3rd son, SadAshiva's request MahAkAli similarly created from herself Bhuvanasundari or Bhuvaneswari. Alongwith Bhuvaneswari Lord Shiva got engaged in the task of destruction. In this fashion further 4 more MahAvidyas were created.
NirvAna Tantram Patala 1.
So, with AdyA MahAkali the number turns out to be 8.
In the Vaishnava PanchaRAtra text called Lakshmi Tantram, MahAsarswati has been mentioned as a MahAvidyA (in 4th patala) and Niyati Devi too (in 7th patala).
As per Tantrakaumidi, ChAmundA, Gauri, PratyangirA and KAtyAyani are also MahAvidyAs.
In VAravAnaliya Tantram MahAvidyA's Amnaya bhedas are given viz:
DakshinAkAli, BagalAmukhi, ChinnamastA, TArA, and BhadrA belongs to the Southern Amnaya. MAtangi- Western Amanya. DhumrAvati- Northern Amanya. Shodashi and Bhairvi- Upper (Urdha) Amanya. Bhuvaneswari, Lakshmi, Saraswati and Annapurna are all Devis of the Eastern Amanya.
According to Niruttara Tantram there are 18 MahAvidyas viz:
KAli tArA tatha chinna matangi bhuvaneswari |
AnnapurnA tathA nityA durgA mahishamardini ||
TwaritA tripurA putA bhairavi bagalA tathA |
dhumAvati tathA jneya kamala cha saraswati ||
JayadurgA tathA bhadre tatha tripurasundari |
Ashtadasha mahAvidya tantrAdau kathita priye ||
However, according to NArada PancharAtra the number of MahAvidyas is 7 crores and upavidyas are equally numerous. Their forms can not be counted.
SaptakotirmahAvidyA upavidyAshcha tadrishAh |
TAsAm murtimunisreshtha sankhyAtum naiva shakyate ||
But there's a significance of the number 10 with respect to the MahAvidyas as told by Lord SadAshiva in MahAnirvana Tantram:
Just like the number 0 in itself does not have any value and can regarded as indicative of the formless infinite. So is the Parabrahmayi ParAdevi. But just as when prefixed with a 1 it (0) makes the number 10, similarly when the ParAdevi (0) conjoins with her own trigunAtmika prakriti (or 1) she appears as the 10 MahAvidyAs to fulfill the wishes of the devotees.
According to personalities (guna) and activity (kriyA) different forms of ParAdevi has been imagined.
GunakriyAnusarena rupam devyAh prakalpitam - MahAnirvana Tantram 13.4