Can one worship of The God without idols?
already written in vedas as na tasya pratimā asti yasya nāma mahadyaśaḥ ।
Is it necessary to worship of idols ? Can one worship of The God without idols ?
Let me start my answer by firstly explaining why idol worship of gods came into existence. Its said in Shreemad Bhagvat Purana that in the beginning of Treta yuga saints ,sages introduced deity worship in the form of idols when they saw people are doing Disdain (Tiraskar ) , Malice and disrespecting each other .
दृष्ट्वा तेषांमिथो नृणामवज्ञानात्मतां नृप |
त्रेतादिषु हरेरर्चा क्रियायै कविभि: कृता ||३९||
dṛṣṭvā teṣāṁ mitho nṛṇām avajñānātmatāṁ nṛpa
tretādiṣu harer arcā kriyāyai kavibhiḥ kṛtā
My dear King, when great sages and saintly persons saw mutually disrespectful dealings at the beginning of Tretā-yuga, Deity worship in the temple was introduced with all paraphernalia. SB 7.14.39
Here in this shloka Shree Krishan is telling us the methods by which worship is done to him.
Shree Krishan said -:
वैदिकस्तान्त्रिको मिश्र इति मे त्रिविधो मख: |
त्रयाणामीप्सितेनैव विधिना मां समर्चयेत ||७||
vaidikas tāntriko miśra iti me tri-vidho makhaḥ
trayāṇām īpsitenaiva vidhinā māṁ samarcaret.
One should carefully worship Me by selecting one of the three methods by which I receive sacrifice: Vedic, tantric or mixed.SB 11.27.7
द्रव्यै: प्रसिद्भैर्मदयाग: प्रतिमादिष्वमायिन: |
भक्तस्य च यथालब्धैर्ह्यदि भावेन चैव हि ||१५||
dravyaiḥ prasiddhair mad-yāgaḥ pratimādiṣv amāyinaḥ
bhaktasya ca yathā-labdhair hṛdi bhāvena caiva hi
One should worship Me in My Deity forms by offering the most excellent paraphernalia. But a devotee completely freed from material desire may worship Me with whatever he is able to obtain, and may even worship Me within his heart with mental paraphernalia. SB 11.27.15
अर्चादिषु यदा यत्र श्रद्भा मां तत्र चार्चयेत |
सर्वभूतेषश्वात्मानि च सर्वात्माहमव्यवस्थित: ||४८||
arcādiṣu yadā yatra śraddhā māṁ tatra cārcayet
sarva-bhūteṣv ātmani ca sarvātmāham avasthitaḥ
Whenever one develops faith in Me — in My form as the Deity or in other bona fide manifestations — one should worship Me in that form. I certainly exist both within all created beings and also separately in My original form, since I am the Supreme Soul of all. SB 11.27.48
Conclusion – So from analyzing obove shlokas , we can say that both forms of worship are the same (Saguna and Nirguna). So its not necessary that gods should only be worshiped in deity form (Idol worship).One can worship god through Mind and Heart also.
Can one worship of The God without idols?
Yes, Gods can be invoked and worshiped in as many as ten places among which idol is just one such place.
The different ten places are given in the following verses from the KulArnava Tantram, which is a Shakta Agama Shastra.
Linga SthandilaVahnyamvusurpa Kubhyapateshu Cha |
Mandale Phalake Muddhni Hrudi VA Dasha KirtitA ||
Eshu SthAneshu Devesi Yajanthi Paramam ShivAm |
ArupAm Rupinim KritvA Karma KAndaratA NarAha ||
Kularnava Tantram, Chapter 6, Verses 74-75.
Lord Shiva said :
The worshiper visualizes the Formless Devi Parama Shiva in Form and adores Her in the linga, sign-symbol, altar, Fire, Water, winnowing fan, wall, image/idol , Mandala (diagram), plank, in the head or in the heart. These ten places are known to be the different places of worship.
So, as you can see, Gods can be invoked in fire (as is done in fire ritual or Homa), water (Ambu, as we do while doing Deva-Rishi-Pitru Tarpanam) and also in one's heart (Hrudi).
There is a definite process of worshiping God within oneself in one's heart. This is called the "Manasa Puja" and can be learned from one's Guru.
So, in short, idol worship is just one of the ways of worshiping Gods but certainly not the only one.
In any case, the reason why God, who is essentially Nirguna (attributeless) and Nirakara (formless), is worshiped in idols having forms is given in the following verse of the same Scripture.
ChinmayasyAprameyasya NirgunasyA Saririnaha |
SAdhanAm HitArthaya Brahmano RupakalpanA ||
KulArnava Tantram, Chapter 6, Verse 73.
The Brahman is indeed the Immeasurable, the Impersonal, without attribute, a sheer Consciousness. Yet for the benefit of the aspiring, of those who seek for It, Brahman assumes forms, determines Itself in a way as to be cognisable and accessible. It takes Form but certainly It is not limited by that Form or any number of Forms.
So, you can invoke & worship Lord Shiva or Sri Hanumana in your own heart, or in fire or in water. And you need not require idols for your worship then.
BTW, if you are not aware of the term Shakta Agama, then Shakta denotes the devotees of Shakti or Mother Goddess and for knowing what Scriptures are denoted by Agama, you can see this answer or this wikipedia page.