Lord Shiva forms the basis of creation of everything and it is also represented by his AshtaMurti or Eight Fold forms.
1) AshtaMurti in Vedas:
RigVeda states Lord Shiva as 'Pururupa' or 'one who has multiple forms.' and RigVeda also states 'Yajatam Vishwarupam' ie. Who himself is in the form of Whole world. Similarly SataRudriyam section of Yajurveda which is a hymn to Lord Shiva also states:
विरुपेभ्यो नमो विश्वरुपेभ्येश्चभो नमोः
Salutations to him who is formless and whose form is the Entire Universe (VishaRupam)
And the Brahmanas of Vedas give detailed explanations on what AshtaMurti represent. In the Kaushitki Brahmana of RigVeda, origin of AshtaMurti forms take place through Lord Brahma (Prajapati);
Prajapati made a golden bowl an arrow breadth in height and similar in breadth, in it he poured the seed, than arose he of thousand eyes, thousand feets and thousand fitted.
He grasped his father Prajapati, he said to him why do you grasp me? He replied give me a name assigned for without name assigned I shall not eat food here.
Then Prajapati goes on speaking Eight names and their significances too:
He answered, ‘You are Bhava.’ Since the waters are Bhava, thereby Bhava harms him not, nor his offspring, nor his cattle, nor any one claiming to be his. ..... He answered, ‘You are Sarva.’ Since the Fire is Sarva, thereby Sarva harms him not, not his offspring, not his cattle nor any one claiming to be his..... He answered. ‘You are Pashupati’ Since Air is Pashupati, Pashupati harms him not, not his offspring, not his cattle, nor any one claiming to be his..... He answered, ‘You are Ugra‘ Since the plants and trees are Ugra, thereby Ugra harms him not, nor his offspring, nor his cattle, nor my one claiming to be his.... He answered, ‘ You are Mahadeva’ Since the sun is Mahadeva, thereby the Mahadeva harms him not, nor his offspring, nor his cattle, nor any one claiming to he his.... He answered, ‘You are Rudra.’ Since the moon is Rudra, thereby Rudra harms him not, nor his offspring, nor his cattle, nor any one claiming to he his.... He answered, ‘You are Ishana'. Since food is Ishana thereby Ishana harms him not, nor his offspring, nor his cattle, nor any one claiming to be his.... He answered, 'You are the Ashani.' Since Indra is the Ashani thereby the Ashani harms him not, not his offspring, nor his cattle, nor any one claiming to be his..... (RigVeda Kaushitki Brahmana chapter 6)
Thus the AshtaMurti as per Kaushitki Brahmana of RigVeda are:
Bhava ➡ Water
Ugra➡Plant and Trees (Earth element) Mahadeva➡Sun
Thus as per Kaushitki Brahmana the Eight Forms or Astamurti are Fire, Water, Air, Food, Plants, Sun, Moon and Indra.
In the YajurVeda Shatapatha Brahmana also Lord Shiva taking AshtaMurti form is described through his Agni form.. Just after birth from Prajapati he cries than Prajapati begins to give name to him along with it's significance:
He said to him, 'You are Rudra' And because he gave him that name, Agni became suchlike (or, that form), for Rudra is Agni: because he cried (rud) therefore he is Rudra..... He said to him, 'You are Sarva.' And because he gave the him that name, the waters became suchlike, for Sarva is the waters, inasmuch as from the water everything here is produced... He said to him, 'You are Pasupati.' And because he gave him that name, the plants became suchlike, for Pasupati is the plants: hence when cattle (pasu) get plants, then they play the master (patîy)..... He said to him, 'You are Ugra.' And because he gave him that name, Vâyu (the wind) became suchlike, for Ugra is Air hence when it blows strongly, they say 'Ugra is blowing.'.... He said to him, 'You are Asani.' And because he gave him that name, the Vidyuta (lightning) became suchlike, for Asani is Vidyuta hence they say of him whom the lightning strikes, 'Asani has smitten him.'.... He said to him, 'You are Bhava.' And because he gave him that name, Parjanya became suchlike; for Bhava is Parjanya, since everything here comes (bhavati) from the rain-cloud...
He said to him, 'You are MahaDeva.' And because he gave him that name, the moon became suchlike, for the moon is Pragâpati, and Pragâpati is Mahadeva ..... He said to him, 'You are Ishana (the Ruler).' And because he gave him that name, the Sun became suchlike, for Ishana is the Sun, since the Sun rules over this All. He said, 'So great indeed I am: give me no other name after that!' (YajurVeda Shatapatha Brahmana)
Thus AshtaMurti as per Shatapatha Brahmana are:
Ashani ➡Vidyuta (Electricity/Lightning)
Sayana in commentary of Shatapatha Brahamana states that Parjanya denotes Yajamãna and Vidyuta denotes Aakash element:
Vegetation is called ‘paśupati’ since animals derive strength from it. Or when animals ‘attain’, ‘eat’ vegetation they become lords. Those who are full of desire, they long to attain their lords. Hence the vegetation is
the desire-fulfilling entity for the animals, it, Ośadhi, is called paśupati. From this, the element ‘bhūḥ’, Earth, has been stated. Since the lightning happens in the ‘ākāśa’.... by the word ‘vidyut’, the space-form of Rudra is being stated ....... The word ‘bhava’ denotes parjanya, rain. By this name, the ‘yajamāna’ form is stated. He indeed is the one who harbors all desires and therefore ‘bhavatva’ is appropriate for him..... (Sayana Commentary)
Thus AshtaMurti as per Shatapatha Brahmana are:
Fire, Water, Air, Earth, Space, Moon, Sun, Yajamãna
There are some variations in Kaushitki Brahmana and Satapatha Brahmana but when there is variations/contradiction in Shruti both things are accepted.
So, the AshtaMurti represents:
Fire, Water, Air, Space (Vidyuta), Earth( Plants), Food, Sun, Moon, Yajamãna (Parjanya), Prajapati, Indra
2) Ashtamurti in Mahabharata:
In the Harivamsha Parva of Mahabharata, AshtaMurti forms of Lord Shiva are stated as:
यं विधुर्भूततत्त्वज्ञं भूतेषं भूतभावनम् ।
वामदेवं विरूपाक्षमाहुस्तत्त्वविदो जनः ॥३-८५-१७
महादेवं सहस्राक्षं कालमूर्तिं चतुर्भुजम् ।
रुद्रं रोदननामानमाहुर्विश्वेश्वरम् शिवम् ॥३-८५-१८
अप्रमेयमनाधारमाहुर्माहश्वरा जनाः ।
नग्नं नग्नपरीतं तु नागिनम् त्वग्निवर्चसम् ।३-८५-१९
आहुर्विश्वेश्वरं शान्तं शिवमादिं सनातनम् ।
तस्य मूर्तिरिमाः सर्वा धराद्याः सकला नृप ॥३-८५-२०
भूमिरापोऽनलो वायुः खं सूर्यश्च तथा शशी ।
अग्निश्च यजमानश्च प्रकृतिश्चैवमष्टधा ॥३-८५-२१
The wise people, knowledgeable about the fundamental principles say that the lord is the basic principle of beings, the lord of beings, the lord who is concerned with the welfare of the beings, lord vAmadeva and the lord with the
third eye. The great lord, the lord with thousand eyes, the lord of time, the lord with four arms, rudra and rodana, the lord of the world, the auspicious lord. The people say that the great lord is immeasurable and devoid of supports. The unconcealed lord has unconcealed followers. The lord, surrounded by serpents has the lustre of fire. He is called Vishveshvara, Tranquil, Auspicious, the Primal Ancient One. All that is seen in creation is His form. The earth, water, fire, wind, sky, sun as well as moon and the god of fire as the institutor of the sacrifice (yajamAna) -- These are the eight-fold natural forms of the Lord.
3) AshtaMurti in Puranas:
i) Shiva Purana:
Shiva Purana states of Ashtamurti forms many many times. For eg in ShatRudraSamhita 2nd chapter:
शर्वो भवस्तथा रुद्र उग्रो भीम पशोः पति ।
ईशानश्च महादेवो मूर्तयश्चाष्ट विश्रुता ।।
अधितिष्ठाश्च शर्वाद्यैरष्टरुपैः शिवस्य हि ।।
The well known eight presiding deities are Sarva, Bhava, Rudra, Ugra, Bhima, Pashupati, Ishana and Mahadeva. These eight preside over Earth, Water, Fire, Wind, Sky, Soul, Sun and Moon.
ii) Vishnu Purana:
Vishnu Purana also gives similar account like that of Shatapatha Brahamana episode:
एवमुक्तः पुनः सोऽथ सप्तकृत्वो रुरोद वै।
ततोऽन्यानि ददौ तस्मै सप्त नामानि वै प्रभुः।
स्थानानि चैषामष्टानां पत्नीः पुत्रांश्च वै प्रभुः।। ५ ।।
भवं सर्व महेशानं तथा पशुपति द्विज।
भीममुग्रं महादेवं उवाच स पितामहः।। ६ ।।
चक्रे नामान्यथैतानि स्थानान्येषां चकार सः।
सूर्यों जल मही वहिर्वायुराकाशमेव च।
दीक्षितो ब्राह्मणः सोम इत्येतास्तनवः क्रमात्॥७॥
(Vishnu Purana 1.8)
But, thus addressed, the boy [Rudra] still wept seven-times, and Brahma therefore gave to him seven other denominations; and to these eight persons, regions and wives and posterity belong. The eight manifestations, then, are named Rudra, Bhava, Sarva, Ishana, Pasupati, Bhima, Ugra and Mahādeva, which were given to them by their great progenitor. He also assigned to them their respective stations, the Sun, water, ether, air, fire, earth, the ministrant Brahman, and the moon; for these are their several forms.
iii) Markandeya Purana:
Markandeya Purana also gives similar account:
(He said): - Thou, O Deva or Bright One, shall be of the name of Rudra. Do not cry. Be patient. Thus spoken to, then he cried again and again seven times. Then to him the lord gave seven other names, and also the abodes of these eight Rudras, and their wives and sons, O thou twice-born one, (were duly assigned). The lord, the Grand-father (Brahma), spoke and gave these names, - namely Bhava, Sarva, similarly Ishana, likewise Pashupati, Bhima, Ugra, Mahadeva and made abodes for these. The sun, the water, the earth, the fire, the ether, the initiated Brahman, and the moon, these became respectively their abodes. [Chapter 52]
And so on in other many Puranas too similar description are found.
4) AshtaMurti Invocations in Grihya Sutras:
Invocation of AshtaMurti forms is very popular in Grihya Sutras. Baudhayana Grihya Sutra 2.7, Hiranyakeshi Grihya Sutra 2nd Patala, Agniveshya Grihya Sutra 5th chapter, Bharadvaja Grihya Sutra 2nd Prashna, Vaikhasana Grihya Sutra 4th Prashna offer to AshtaMurti forms as:
भवाय देवाय स्वाहा शर्वाय देवाय स्वाहा ईशानाय देवाय स्वाहा पशुपतये देवाय स्वाहा रुद्राय देवाय स्वाहा उग्राय देवाय स्वाहा भीमाय देवाय स्वाहा महते देवाय स्वाहा इति। भवस्य देवस्य पत्न्यै स्वाहा शर्वस्य देवस्य पत्न्यै स्वाहा ईशानस्य देवास्य पत्न्यै स्वाहा पशुपतेर्देवस्य पत्न्यै स्वाहा रुद्र देवस्य पत्न्यै स्वाहा उग्रादेवस्य पत्न्यै स्वाहा भीमदेवस्य पत्न्यै स्वाहा महते देवस्य पत्न्यै स्वाहा इति।
Offerings be to divine Bhava, To Sharva, To Ishana, To Pashupati, To Rudra, To Ugra, To Bhima, To Mahadeva. Offerings be to wife of Bhava, wife of Sharva, wife of Ishana, wife of Pashupati, wife of Rudra, wife of Ugra, wife of Bhima, wife of Mahadeva....
5) AstaMurti Invocation in Veda Samhitas:
AshtaMurti forms are also mentioned in Veda Samhitas like:Taittariya Samhita 1.4.36, Shukla YajurVeda 39th chapter, AtharvaVeda Vratya Sukta 15.5 and in other places too.
AshtaMurti description in various stotras/works:
1) Tirumular in Tirumantiram:
The One is He, the Two His sweet Grace, In Three He stood, in all the Four witnessed, The Five He conquered, the Six He filled, The Seven Worlds pervades, manifests the Eight And so remains.
2) Kalidasa in Abhijnanasakuntalam:
May the Lord protect you, the Lord endowed with eight visible bodies, viz., - the one that represents the first creation of the creator (water), the one which transports materials duly offered in the fire (fire), the one which represents the sacrificer (soul), the two which create time (the Sun and the Moon), the one which, being imbued the quality capable of being sensed by the ear, stands pervading the Universe (ether), the one which the wise men declare the root cause of all elements (earth) and the one by which living beings are animated by life (air). [Invocation prayer]
3) Pushpadanta in Mahmina stotram:
त्वमर्कस्त्वं सोमस्त्वमसि पवनस्त्वं हुतवहः
त्वमापस्त्वं व्योम त्वमु धरणिरात्मा त्वमिति च।
परिच्छिन्नामेवं त्वयि परिणता बिभ्रति गिरं
न विद्मस्तत्तत्त्वं वयमिह तु यत् त्वं न भवसि॥ २६॥
You are the sun, the moon, the air, the fire, the water, the sky (ether/space), and the earth (the five elements or `bhUtA's). You are the Self which is omnipresent . Thus people describe in words every attribute as yours . On the other hand, I do not know any fundamental principle or thing or substance, which you are not!
भवः शर्वो रुद्रः पशुपतिरथोग्रः सहमहान्
तथा भीमेशानाविति यदभिधानाष्टकमिदम्।
अमुष्मिन् प्रत्येकं प्रविचरति देव श्रुतिरपि
प्रियायास्मैधाम्ने प्रणिहित-नमस्योऽस्मि भवते॥ २८॥
I salute you as the dear abode of the following 8 names: bhava, sharva, rudra, pashupati, ugra, mahadeva, bhiima, and Ishaana; the `Vedas' also discusses individually about these names.
4) Adi Shankara in Dakshinamurty stotram:
भूरम्भांस्यनलोऽनिलोऽम्बरमहर्नाथो हिमांशु पुमान्
इत्याभाति चराचरात्मकमिदं यस्यैव मूर्त्यष्टकम्
नान्यत् किञ्चन विद्यते विमृशतां यस्मात्परस्माद्विभोः
तस्मै श्रीगुरुमूर्तये नम इदं श्रीदक्षिणामूर्तये ॥९॥
Earth, Water, Fire, Air, Space, Sun, Moon and Jiva are Verily His Eight Manifestations Shining within the Moving and the Non-Moving forms, Apart from Him there Cannot Exist anything; The Yogis who Reflect (i.e. Meditate) within Discover Him as the Essence From Which Everything Originates, ... Discover Him as Existing Beyond Everything as the Eternal Essence. Salutations to Him, the Personification of Our Inner Guru Who Awakens This Knowledge through His Profound Silence; Salutation to Sri Dakshinamurthy.
5) Sri Abhinavagupta in TantrasAra:
स च अष्टधा-क्षितिजलपवनहुताशनाकाशसोमसूर्यात्मरुपासु अष्टासु मूर्तिषु मन्त्रन्यासमहिम्ना परमेश्वररुपतया भावितासु तादात्म्येन च देहे परमेश्वरसमाविष्टे शरीरादिविभागवृत्तेः चैतन्यस्यापि परमेश्वरसमावेशप्राप्ति: (12th chapter)
Furthermore, this absorption is eightfold. By means of meditation on the very nature of Paramesvara, and by the power of the placement of the mantras (nyasa) in the eightfold form of Siva, i.e., the earth, water, air, fire, ether, moon, sun, and the self (atma), and in one's own body by gaining identity with it. one becomes firmly absorbed in Paramesvara. In this way, a limited soul, which functions differently as a body, etc., attains absorption in the Lord.
6) Patanjali in Nataraja Stotram:
अनन्तमहसं त्रिदशवन्द्य चरणं मुनि हृदन्तर वसन्तममलम्
कबन्ध वियदिन्द्ववनि गन्धवह वह्निमख बन्धुरविमञ्जु वपुषम् ।
अनन्तविभवं त्रिजगन्तर मणिं त्रिनयनं त्रिपुर खण्डन परम्
सनन्द मुनि वन्दित पदं सकरुणं पर चिदम्बर नटं हृदि भज ॥ ५॥
His might endless, the gods bow down to his feet. He brings Spring to the heart of the saints. He is Perfect. Water, sky, moon, earth, wind, fire, Atma, sun make his lovely form. His majesty is endless. He is the most precious of the three worlds. Three-eyed, he is inclined on destroying Tripura. Saint Sananda bows to his feet. He is merciful.
Significance of AshtaMurti Form:
These Eight forms of Lord Shiva are also of great significance.
1) Significance in creation itself:
The creation itself became 'Suchlike' or attained form due to AshtaMurti forms. It's described in YajurVeda Satapatha Brahmana as;
... Fire became suchlike for Rudra is fire... Water became suchlike for Sarva is water...
Plants became suchlike for Pashupati is plants... Air became suchlike for Ugra is air.
... Vidyuta became suchlike for Ashani is Vidyuta... Moon became suchlike for Mahadeva is moon... Sun became suchlike for Ishana is sun (YajurVeda Shatapatha Brahmana 6.1)
Thus the whole creation came into existence due to manifestation of AshtaMurti forms.
2) Prevention from Harm:
Realising that these AshtaMurti things belongs to Shiva is necessary so that one doesn't get harmed by these things:
the waters are Bhava, thereby Bhava harms him not, nor his offspring, nor his cattle, nor any one claiming to be his. ...Fire is Sarva, thereby Sarva harms him not, not his offspring, not his cattle nor any one claiming to be his.... Air is Pashupati, Pashupati harms him not, not his offspring, not his cattle, nor any one claiming to be his..... Ugra harms him not.... sun is Mahadeva, thereby the Mahadeva harms him not, nor his offspring, nor his cattle, nor any one claiming to be his... moon is Rudra, thereby Rudra harms him not.... food is Ishana thereby Ishana harms him not,.... Indra is the Ashani thereby the Ashani harms him not, not his offspring, nor his cattle, nor any one claiming to be his..... (RigVeda Kaushitki Brahmana chapter 6)
Thus one should realise that these things like Sun, Moon, Air, Water, Fire etc... are Shiva so that he isn't harmed by these things also.
3) Naming and name chanting:
Shatapatha Brahmana episode gives extra injunction teaching (which is not present in Kaushitki Brahamana), the injunction is about name giving to a baby and Prajapati tells that giving name to a new born baby frees one from evil and after saying it he starts to pronounce AshtaMurti names.
Pragâpati said to him, 'My boy, why criest thou, when thou art born out of labour and trouble?' He said, 'Nay, but I am not freed from (guarded against) evil; I have no name given me: give me a name!' Hence one should give a name to the boy that is born, for thereby one frees him from evil; --even a second, even a third (name), for thereby one frees him from evil time after time.
Actually Rudra in the [form of Agni] is born this time with the union of Prajapati and Usha, this union is sin in Gods eye. As described here Rudra punished Prajapati, but this time during birth Rudra makes Prajapati pronounce his Eight names by saying as if he himself is not freed from evil and in this way Prajapati escaped from punishment of Rudra this time.
Thus it is also recommended to give AshtaMurti names to a baby. Similarly chanting of AshtaMurti names is also very fruitful because all these names are present in SataRudriya section of YajurVeda and as Jabala Upanishad states one gets immortality by chanting names of Sata Rudriya:
III-1. Then the discipline students (Brahmacharins of Yajnavalkya) asked him: ‘Pray, tell us, what is that mantra by reciting which one attains immortality ?’ He replied: ‘By (reciting) Satarudriya’. These mantras are indeed the names of (Rudra to achieve) immortality. By (reciting) these (mantras) one becomes immortal.
4) Harming others is like Harming Shiva:
Since, Shiva is present in every form of creation so, harming or insulting creation or persons is like Harming or insulting Shiva himself. Shiva Purana ShatRudra Samhita chapter 2 states:
क्रियते यस्य कस्यापि देहिनो यदी निग्रहः ।
अष्टमूर्तेरनिष्टं तत्कृतमेव न संशय ।।
अष्टमूर्त्यात्मना विश्वमअधिष्ठायास्थितं शिवम् ।
भजस्व सर्वभावेन रुद्र परमकारणनम् ।।
In case if some damage or bondage is caused by one person to another person, than he surely does harm through AshtaMurti who is the presiding form of Shiva, who should always be adored because Shiva happens to be the primordial cause of all.
5) Realisation of whole Universe as Shiva:
By contemplating on AshtaMurti forms one can realise 'Sarva khalvidam Brahman' ie. 'Whole Universe is Brahman' itself. Shiva Purana states:
प्रत्ययार्थं च जगतामेकस्थोऽपि दिवाकर ।
ऐकोऽपि बहुदा दृष्टो जलधारादिवस्तुषु ।।
दृश्यते श्रुयते लोके यद्यत्सदसदात्मकम् ।
तत्तत्सर्वं सुरा वित्तं परं ब्रह्म शिवात्मकम् ।। (Rudra Samhita Shristi khanda chapter 12)
A single sun in order to convince the world appears in several ways in pitchers filled with water. Similarly whatever is Sat and Asat in the world, O Gods, should be taken as the form of Shiva.
Similar Vedantic truth through realisation of AshtaMurti is brought by Kalidasa in the invocation of his famous work Abhijnana Shakuntalam:
या स्रिष्टिः स्रुष्टुराद्या वहति विधिहुतम् या हविर्या च होत्री।
ये द्वे कालम् विधत्तः श्रुतिविषय गुणाः या स्थिता व्याप्य विश्वम्।।
याम् आहुः सर्वबीजप्रकृतिरिति यया प्राणिनः प्राणवन्तः।
प्रत्यक्षाभिः प्रपन्नस्तनुभिरवतु वस्ताभिरष्टाभिरीशः।।
May the Lord protect you, the Lord endowed with eight visible bodies, viz., - the one that represents the first creation of the creator (water), the one which transports materials duly offered in the fire (fire), the one
which represents the sacrificer (soul), the two which create time (the Sun and the Moon), the one which, being imbued the quality capable of being sensed by the ear, stands pervading the Universe (ether), the one which the wise men declare the root cause of all elements (earth) and the one by which living beings are animated by life (air).
Thus contemplating on the AshtaMurti forms one reaches to the conclusion that 'Sarvam Shivamayam Jagat' or 'Entire Universe is Shiva.'
For eg. Contemplating on a rain drop coming from sky and with respect to Shatapatha Brahamana description:
That rain drop is water which itself is AshtaMurti form of Sharva. Fire element ie. Heat (Rudra) present in that drop is making liquid form of water to exist. Water drop is occupying some space to exist (Ashani). Water is made of two air molecules (Ugra). Water molecules contains many electromagnetic forces (Ashani =Vidyuta). There is also solidity in water molecules eg. like in nucleus (Pashupati). Our mind (Mahadeva) is observing that. That water drop when strikes seeds grow plants (Pashupati). From it comes food (Ishana). Previously also that water came from sea (Sarva). It was heated (Rudra) by Sun (Ishana). It became vapour (Ugra), it went to sky (Bhima). Lightning (Ashani) came there. Rainfall (Parjanya = Bhava) occurred there and it fell towards earth (Pashupati). Time is continuously flowing while this event is happening and can be represented through Sun (Ishana) and Moon (Mahadeva)...
Thus contemplating on this way one can experience AshtaMurti forms of Shiva in minute minute things also. And finally Sri Rudram comes which states Lord Shiva himself is every form of creation. And also comes declaration of Taittariya Aranyaka (10.24,25) of YajurVeda:
सर्वो वै रुद्रस्तस्मै रुद्राय नमो अस्तु । पुरुषो वै रुद्रः
सन्महो नमो नमः । विश्वं भूतं भुवनं चित्रं बहुधा जातं जायमानं चयत् । सर्वो ह्येष रुद्रस्तस्मै रुद्राय नमो अस्तु ॥
All this verily is Rudra. To Rudra who is such we offer our salutation. We salute again and again that Being, Rudra, who is Purusha. The material universe the created beings and whatever there is manifoldly and profusely created in the past and in the present in the form of the world, all that is indeed this Rudra. Salutations be to Rudra who is such.
And finally I want to close this answer with the Eight forms mentioned in Svetasvatara Upanishad:
स्तद्वायुस्तदु चन्द्रमाः ।
तदेव शुक्रं तद् ब्रह्म
तदापस्तत् प्रजापतिः ॥ 4.2॥
That Supreme Self is Agni (Fire); It is Aditya (Sun); It is Vayu (Wind); It is Chandrama (Moon). That Self is the luminous stars; It is Hiranyagarbha; It is water; It is Virat.