Emergence of various forms Deities in Hinduism
Hinduism recognizes the diverse aspects of personalities and personal preferences. Worshipping or prayer of god has its root in human desires.  Various deities in Hinduism address the different aspects of human desires. For instance, Lakshmi ji is worshipped for wealth & prosperity, Sarasvati ji is worshipped for knowledge & various discipline of art, Durga ji is worshipped for power & valor, Ganesha ji is worshipped mainly to overcome obstacles, Hanuman ji is worshipped mainly for strength,   Shiva represents austerity and so on. Hence, the Hinduism offers more than one options for worshipping and creating personal bond. This can be seen in parallel with the growth of general management system to specialized management system in corporate world for better results.
 
Since Vedic times, many forms of this divinity have been idolized such as deities of nature (Indra, Agni, Soma, Surya etc.); 33 koti deities (eight Vasus, eleven Rudras, twelve Adityas, Indra and Prajapathi Brahma); Trimurti (Brahma, Vishnu & Shiva), Panchparmeshvar (Shiva, Vishnu, Devi or Parvati, Surya and an Ishta Devata) and Vaishnava Avtars (mainly Rama & Krishna).
 
However, Hinduism fundamentally, establishes that there is only Brahman or one all-pervasive God or cosmic consciousness which energizes the entire universe and also deities.
 
Emergence of various forms of deities is discussed as below:
 
Vedic Deities:

1. During Vedic period (over 5000 years ago), people did not worship images or idols but gods of nature. Vedic people did not build any temples to house their gods.
2. There was no supreme deity. The gods in the Rig-Veda fall into two categories: the devas – who were gods of nature – such as the weather deity Indra (who is also the King of the gods), Agni ("sacrificial fire"), Usha ("dawn"), Surya ("sun") and Apas ("waters") on the one hand, and on the other hand the asuras – gods of moral concepts – such as Mitra ("contract"), Aryaman (guardian of guest, friendship and marriage), Bhaga ("share") or Varuna, the supreme Asura (or Aditya). Devas are characterised as Younger Gods while Asuras are the Older Gods.
3. In later Vedic texts, the Asuras become demons. Gradually, dominance of four-fold godhead namely Indra (associated with storm), Agni, Soma (plant of immortality i.e. amurta) and Surya (or aditya) emerged. Extensive hymns were consecrated to these gods in the Rig Veda.
4. Philosophically, Vedic gods represent symbols of inner self (antahkaran) such as Sun symbolises to intellect, Agni to volition, Soma to feelings etc.

33 Koti Deities
In Brihadaranyaka Upanishad, it is mentioned that 33 koti deities as the important ones, namely eight Vasus, eleven Rudras, twelve Adityas, Indra and Prajapathi Brahma. These gods belong to different sphere in creation.
Note:
Please also see related article on my website named as “what is God in Hinduism” published on 19.06.2018 under the category “Principles”.
 
Trimurti or Trinity Deities
The triad (trimurti or trinity or Brahma, Vishnu & Shiva) appears in Maitrayaniya Upanishad, for the first time. From the 1st century CE a new type of worship known as Bhakti or devotional Hinduism spread across the Indian sub-continent, and the old Vedic gods were replaced in importance by deities like Shiva, Vishnu, Brahma, and Devi. Their worship required temples where the devoted could offer their thanks which led to construction of elaborate temples.
 
 Supreme Brahman:

1. Major Upanishads like Brihadaranyaka, Ishavasya, Chandogya, Katha, Kena, Aitareya, do emphasize on the knowledge of Brahman as essential to liberation.
2. Sri Adi Shankaracharya (788-820) established Advaita (Non-duality of Supreme Brahman) interpretation of Vedanta which has its roots at least to Gaudapada (600 CE). 

 
Panch-Parmeshwar

1. Five deities being Shiva, Vishnu, Devi or Parvati, Surya and an Ishta Devata such as Kartikeya or Ganesha or any personal god of devotee's preference. It became popular in medieval period which has been attributed to Adi Shankara, the 8th century CE.
2. The Puranas provide insight into the aspects of idol-worship, festivals and devotions. There are 18 Mahapuranas and an equal number of subsidiary Puranas or Upa-Puranas and many 'sthala' or regional Puranas. Of the 18 major texts,
   1.         six glorify Vishnu; six glorify Brahma; and six glorify Shiva viz. Vaishnava aspects - Vishnu Purana, Naradiya Purana, Bhagavat Purana, Garuda Purana, Padma Purana, Varaha Purana;
   2. Brahma as central deity - Brahma Purana, Brahmanda Purana, Brahma-Vaivarta Purana, Markandeya Purana, Bhavishya Purana, Vamana Purana;
   3. Shaivite aspects -  Matsya Purana, Kurma Purana, Linga Purana, Shiva Purana, Skanda Purana and Agni Purana.
3. In Markandeya Purana, glorification of goddess is recognized under all major aspects. This led to traditions of Vaishnavism, Shaivism, Shaktism, and Smarthism.
4. The Vaishnavism tradition is known for the loving devotion to an avatar of Vishnu (often Krishna), and it has been key to the spread of the Bhakti movement.
5. In the Shaivism traditions, the followers revere the Shiva as Supreme Being.
6. In the Shaktism tradition, feminine and Adi Parashakti is supreme.
7. In the Smarthism or Smarta tradition treat all the five deities treated as equal – Vishnu, Shiva, Ganesha, Surya and Devi (Shakti).

Vaishnava Avtars

1. During medieval period, Philosophers such as Ramanujacharya, Madhvacharya, Nimbarkacharya, and Vallabhacharya started Various Vaishnava Sampryadaya to worship of Sita-Rama and Radha-Krishna as Sagun Upasna. Even, Adi Shankara who believed to be advocated Jnana marg, also emphasized the importance of devotion and wrote Bhaja Govindam of 33 verses.
2. Vaishnava-inspired scholars authored 14 Vishnu avatar-focused Upanishads that are called the Vaishnava Upanishads. These Upanishads quote the texts included in the Brihadaranyaka Upanishad, Chandogya Upanishad, Katha Upanishad, Isha Upanishad, Mundaka Upanishad, Taittiriya Upanishad and others.
3. The Bhagavad Gita is a central text in Vaishnavism, and especially in the context of Krishna. The two Indian epics, the Mahabharata and the Ramayana also present Vaishnava philosophy and culture.
4. During the 9th-17th centuries, Bhakti poets such as Alwars, Raidas, Narsigh Mehta, Haidas, Meera Bai, Namdev, Ramananda, Surdas, Tulsidas, Eknath, Tyagaraja, Chaitanya Mahaprabhu and many others influenced the expansion of Vaishnavism. They wrote a large number of Bhajans (poetries) in the glory of Parmatama and taught the religion of love and kindness to society.

Note:
Please also see related articles on my website named as “Vaishnava Bhakts” published on 02.03.2018 under the category “Deities, Philosophers and Bhakts” and “Bhakti Yoga” published on 07.03.2018 under the category “Philosophy”.
 
One Supreme God taking multiple forms in Deities

1. Shree Krishna (in chapter 7, verse 21 of Bhagavad Gita) has clarified that whatever deity a devotee chooses to worship with reverence (out of craving for some worldly object), I stabilize the faith of that particular deity/form. He explains that ignorant persons do not understand that the powers of the deities are derived from Brahman i.e. supreme God and Brahman himself gives them the desired fulfilment. Further, he (in verses 9.18, 10.21-23 and 11.15) asserts that the triad or trinity is manifestation of one Brahman.
2. Shree Krishna further, asserts on Vedic Gods (in chapter 10 of Bhagavad Gita), he is Vishnu among the twelve Adityas, Shiva among eleven Rudras, Agni among eight Vasus, the radiant sun among the luminaries, the moon, the lord of the stars, the Indra and essence of so many things.

 
Hence, Nirakar & Nirgun Brahman takes various forms of deities to satiate the needs & desires of human being.
 

Shree Hanuman – the Sankat Mochan
“अतुलितबलधामं हेमशैलाभदेहं दनुजवनकृशानुं ज्ञानिनामग्रगण्यम्‌। कलगुणनिधानं वानराणामधीशं रघुपतिप्रियभक्तं वातजातं नमामि॥“
(Meaning: Atulit Bal Dhaamam - Repository of incomparable strength, Hemshailaabh Deham - whose body resembles a golden mountain, Danujvan Krushanum - destroyer of forces of demons,         Gyaaninaam graganyam - foremost among knowledgeable beings,      Sakal Gun Nidhaanam - repository of all the virtues and good qualities,         Raghupati Priya Bhaktam - dearest of all devotees to Lord Rama, I salute to the son of the wind).
 
Hanuman ji is known as “Sankat Mochan” (remover of problems & liberator from dangers) and great savior. The roles of Hanuman ji find mention in Ramayana. He helped Sugriva to save him from his brother Bali. Hanuman ji as greatest devotee of Shree Rama, played crucial role to find Mata Sita, brought life-saving herb from Himalayas in limited time to save Lakshman ji, killed Ahiravana & rescued Shree Rama and Lakshman and did many notable tasks mentioned in Ramayana. In Kalyug, he is saving the devotees from troubles and therefore is fondly called as Sankat Mochan.
 
Tulsidas ji has highlighted the great deeds in his writings as under:

Hanuman Chalisa:

1. Hanuman ji rendered great service to Sugriva, presenting him to Ram, to get him kingship. (तुम उपकार सुग्रीवहिं कीह्ना । राम मिलाय राज पद दीह्ना ॥१६॥)
2. Vibhishana heeded his counsel and became Lord of Lanka. (तुह्मरो मन्त्र बिभीषन माना । लङ्केस्वर भए सब जग जाना ॥१७॥)
3. Taking refuge in you one finds all delight, those you protect know no fear. (सब सुख लहै तुह्मारी सरना । तुम रच्छक काहू को डर ना ॥२२॥)
4. You are the guardian of saints and sages, the destroyer of demons, the darling of Ram (साधु सन्त के तुम रखवारे । असुर निकन्दन राम दुलारे ॥३०॥)
5. You grant the eight powers (siddhis or supernatural powers named Aṇimā, Garimā, Mahimā, Laghima, Prapti, Prakamya, Isitva, and Vasitva) and the nine treasurers (Nidhis or divine treasures named Mahapadma, Padma, Saṅkha, Makara, Kacchapa, Mukunda, Kunda, Nila and Kharva) by the boon you received from Mother Janaki (अष्टसिद्धि नौ निधि के दाता । अस बर दीन जानकी माता ॥३१॥)
6. Singing your praise, one finds Ram and escapes the sorrows of countless lives. At death, one goes to Ram's own city or is born on earth as God's devotee. Give no thought to any other deity - worshipping Hanuman, one gains all delight. All affliction ceases, all pain is removed, by remembering the mighty hero, Hanuman. (तुह्मरे भजन राम को पावै । जनम जनम के दुख बिसरावै ॥३३॥ अन्त काल रघुबर पुर जाई । जहाँ जन्म हरिभक्त कहाई ॥३४॥ और देवता चित्त न धरई । हनुमत सेइ सर्ब सुख करई ॥३५॥ सङ्कट कटै मिटै सब पीरा । जो सुमिरै हनुमत बलबीरा ॥३६॥)
7. Whoever recites this a hundred times is released from bondage and gains bliss. (जो सत बार पाठ कर कोई । छूटहि बन्दि महा सुख होई ॥३८॥)

 
Sankat Mochan in Hanumanashtak 

In following eight verses in praise of Hanuman were written by Tulsidas wherein he has explained the deeds of Hanuman ji as Sankat Mochan in Hanumanashtak:
 

1. When you were a child, you swallowed the sun believing the sun to be a ripe fruit, plunging the three worlds into darkness. The worlds were in terror and no one could remove this distress. The gods came and entreated you and then you released the sun and ended the suffering. Who in this world doesn't know, O Lord, that your name is Sankat Mochan, the destroyer of suffering? (बाल समय रवि भक्षी लियो तब; तीनहुं लोक भयो अंधियारों; ताहि सों त्रास भयो जग को; यह संकट काहु सों जात  न टारो; देवन आनि करी बिनती तब; छाड़ी दियो रवि कष्ट निवारो; को नहीं जानत है जग में कपि; संकटमोचन नाम तिहारो I को – १)
2. From fear of Bali, king of the monkeys, Sugriva lived on a mountain. Sugriva knew that Bali could not come to that mountain because of the Muni’s curse, yet he still lived in fear. Who else but you could find a solution to this? Seeing Sri Ram coming on the road, you took the form of a Brahmin and brought the Lord to Sugriva, relieving that servant’s suffering. Who in this world doesn't know, O Lord, that your name is Sankat Mochan, the destroyer of suffering? (बालि की त्रास कपीस बसैं गिरि; जात महाप्रभु पंथ निहारो; चौंकि महामुनि साप दियो तब; चाहिए कौन बिचार बिचारो; कैद्विज रूप लिवाय महाप्रभु; सो तुम दास के सोक निवारो I को – २)
3. You went in search of Sita with on Angada, who said, “We'll forfeit our lives if we leave here without bringing news [of Sita]”. Seeing them [the monkeys] all exhausted by the oceans shore, you then brought news of Sita and saved their lives. Who in this world doesn't know, O Lord, that your name is Sankat Mochan, the destroyer of suffering? (अंगद के संग लेन गए सिय; खोज कपीस यह बैन उचारो; जीवत ना बचिहौ हम सो  जु; बिना सुधि लाये इहाँ पगु धारो; हेरी थके तट सिन्धु सबे तब; लाए सिया-सुधि प्राण उबारो I को – ३)
4. Ravana ordered his demonesses to intimidate Sita who said,”Remove my grief!” Just then you, Lord Hanuman, destroyed the mighty demons. When Sita asked the ashoka tree for a spark [to help and her suffering], you dropped the Lord’s ring down to her and removed her suffering. Who in this world doesn't know, O Lord, that your name is Sankat Mochan, the destroyer of suffering? (रावण त्रास दई सिय को सब; राक्षसी सों कही सोक निवारो; ताहि समय हनुमान महाप्रभु; जाए महा रजनीचर मरो; चाहत सीय असोक सों आगि सु; दै प्रभुमुद्रिका सोक निवारो I  को – ४)
5. When an arrow struck Lakshman in the heart, heedless of life you attacked Ravana’s son. You brought the physician Sushena along with his house and uprooted the Drona Peak. Delivering the sajivana herb, you saved Lakshman’s life. Who in this world doesn't know, O Lord, that your name is Sankat Mochan, the destroyer of suffering? (बान लाग्यो उर लछिमन के तब; प्राण तजे सूत रावन मारो; लै गृह बैद्य सुषेन समेत; तबै गिरि द्रोण सु बीर उपारो; आनि सजीवन हाथ  दिए तब; लछिमन के तुम प्रान उबारो I को - ५ )
6. Ravana waged an invisible war and bound Ram and his whole army in nooses of poisonous snakes. Everyone was suffering from this illusion and could not get free. Then you saved them all, O Hanuman, bringing Garuda, the Lord of the birds, who devoured the serpents. Who in this world doesn't know, O Lord, that your name is Sankat Mochan, the destroyer of suffering? (रावन जुध अजान कियो तब; नाग कि फाँस सबै सिर डारो; श्रीरघुनाथ समेत सबै दल; मोह भयो यह संकट भारो; आनि खगेस तबै हनुमान जु; बंधन काटि सुत्रास निवारो I  को – ६)
7. Ahiravana took Ram and his brother Lakshman to Patala, the netherworld, to sacrifice them to the goddess during a puja. Only you could help them by following to the netherworld, rescuing them, and killing Ahiravana and the demon army. Who in this world doesn't know, O Lord, that your name is Sankat Mochan, the destroyer of suffering? (बंधू समेत जबै अहिरावन; लै रघुनाथ पताल सिधारो; देबिन्हीं पूजि भलि विधि सों बलि; देउ सबै मिलि मन्त्र विचारो; जाये सहाए भयो तब ही; अहिरावन सैन्य समेत संहारो I को – ७)
8. Great hero, you have performed many great deeds for the gods. Just think, what hardship is there that a poor wretch like me could have that you cannot remove? Come quickly, O Hanuman and remove all my troubles. Who in this world doesn't know, O Lord, that your name is Sankat Mochan, the destroyer of suffering? (काज किये बड़ देवन के तुम; बीर महाप्रभु देखि बिचारो; कौन सो संकट मोर गरीब को; जो तुमसे नहिं जात है टारो; बेगि हरो हनुमान महाप्रभु; जो कछु संकट होए हमारो I को – ८)
9. With a red body and a shining red countenance, your mighty form is like a lightning bolt, destroying the demons. Glory, glory, glory to you, Lord of the Monkeys! (दोहा: लाल देह लाली लसे, अरु धरि लाल लंगूर; वज्र देह दानव दलन , जय जय जय कपि सूर II)

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During medieval period, philosophers such as Ramanujacharya, Madhvacharya, Nimbarkacharya, and Vallabhacharya started Various Vaishnava Sampryadaya. Vaishnava-inspired scholars authored 14 Vishnu avatar-focussed Upanishads that are called the Vaishnava Upanishads. These Upanishads quote the texts included in the Brihadaranyaka Upanishad, Chandogya Upanishad, Katha Upanishad, Isha Upanishad, Mundaka Upanishad, Taittiriya Upanishad and others.
The Bhagavad Gita is a central text in Vaishnavism, and especially in the context of Krishna. The two Indian epics, the Mahabharata and the Ramayana also present Vaishnava philosophy and culture.
These philosophers established different schools of vedant which are as under:

​
SN    Philosopher       Vedant School    Paramatma              Jivatma (Chit)                     Maya (Jagat)
                                                                  Iswar (Supreme)
1   Shankar Acharya  Advait                   Real, Nirgun             Same as Paramatma           Illusion
       (788-820 AD)
2 Ramanuj Acharya Vishishtadvait      Real, Sagun                   Real                                    Real            
 (1017-1137 AD)                                      (Vishnu or Krishna)        (Both are controlled by Parmatma)                                              
3.Nimbark Acharya  Dvaita-advait          Real                            Real, exist                          Real, exist        
     (1028-1125 AD)                                (Krishna & Radha)         (Both are dependent on Parmatma)                                                                                                  
4.Madhv Acharya    Dvaita                       Real                             Real                                     Real             
     (1294-1317 AD)                                 (Lakshmi Narayan)      (Both are fundamentally different from Ishwar)
5.Vallabh Acharya  Shuddha Dvait          Real                             Real                                      Real               
     (1479-1532 AD)                                (Krishna)         (Different from Ishwar & Clouded by avidya) Power of Ishwar

 Adi Shankaraacharya, Sri Ramanujacharaya, Sri Nimbarkacharaya and Sri Madhvacharaya were conferred title of Jagat guru.​