Monotheism is the belief in a single creator God and the lack of belief in any other Creator. Hinduism is not a monolithic faith and different sects may or may not posit or require such a belief. Religion is considered a personal belief in Hinduism and followers are free to choose the different interpretations within the framework of Karma and reincarnation. Many forms of Hinduism believe in a monotheistic God, such as Krishna followers, Vedanta, Arya samaj, Samkhya school of Vedas etc, Many traditions within Hinduism share the Vedic idea of a metaphysical ultimate reality and truth called Brahman instead. According to Jan Gonda, Brahman denoted the "power immanent in the sound, words, verses and formulas of Vedas" in the earliest Vedic texts. The early Vedic religious understanding of Brahman underwent a series of abstractions in the Hindu scriptures that followed the Vedic scriptures. These scriptures would reveal a vast body of insights into the nature of Brahman as originally revealed in the Vedas. These Hindu traditions that emerged from or identified with the Vedic scriptures and that maintained the notion of a metaphysical ultimate reality would identify that ultimate reality as Brahman. Hindu adherents to these traditions within Hinduism revere Hindu deities and, indeed, all of existence, as aspects of the Brahman. The deities in Hinduism are not considered to be almighty, omnipotent, omniscient and omnibenevolent, and spirituality is considered to be seeking the ultimate truth that is possible by a number of paths. Like other Indian religions, in Hinduism, deities are born, they live and they die in every kalpa (eon, cycle of existence).
In Hindu philosophy, there are many different schools. Its non-theist traditions such as Samkhya, early Nyaya, Mimamsa and many within Vedanta such as Advaita do not posit the existence of an almighty, omnipotent, omniscient, omnibenevolent God (monotheistic God), while its theistic traditions posit a personal God left to the choice of the Hindu. The major schools of Hindu philosophy explain morality and the nature of existence through the karma and samsara doctrines, as in other Indian religions.
Contemporary Hinduism can be categorized into four major traditions: Vaishnavism, Shaivism, Shaktism, and Smartism. Vaishnavism, Shaivism, and Shaktism worship Vishnu, Shiva, and Devi — the Divine Mother — as the Supreme respectively, or consider all Hindu deities as aspects of the formless Supreme Reality or Brahman. Other minor sects such as Ganapatya and Saura focus on Ganesha and Surya as the Supreme. A sub-tradition within the Vaishnavism school of Hinduism that is an exception is dualistic Dvaita, founded by Madhvacharya in the 13th-century (where Vishnu as Krishna is a monotheistic God). This tradition posits a concept of monotheistic God so similar to Christianity that Christian missionaries in colonial India suggested that Madhvacharya was likely influenced by early Christians who migrated to India, a theory that has been discredited by scholars.
The theological interpretation of svayam bhagavān differs with each tradition and the translated from the Sanskrit language, the term literary means "Bhagavan Himself" or "directly Bhagavan." Gaudiya Vaishnava tradition often translates it within its perspective as primeval Lord or original Personality of Godhead, but also considers the terms such as Supreme Personality of Godhead and Supreme God as an equivalent to the term Svayam Bhagavan, and may also choose to apply these terms to Vishnu, Narayana and many of their associated avatars.
In other sub-traditions of Vaishnavism, Krishna is one of many aspects and avatars of Vishnu (Rama is another, for example), recognized and understood from an eclectic assortment of perspectives and viewpoints.
Vaishnavism is one of the earliest single God focussed traditions that derives its heritage from the Vedas. Within Hinduism, Krishna is worshiped from a variety of perspectives.
A different Vaishnavism viewpoint, such as those in Sri Vaishnavism, opposing this theological concept is the concept of Krishna as one of the many avatar of Narayana or Vishnu. The Sri Vaishnavism sub-tradition reveres goddess Lakshmi with god Vishnu as equivalent, and traces it roots its roots to the ancient Vedas and Pancaratra texts in Sanskrit.
^[a] Julius J. Lipner, Hindus: Their Religious Beliefs and Practices, 2nd Edition, Routledge, ISBN978-0-415-45677-7, page 8; Quote: "(...) one need not be religious in the minimal sense described to be accepted as a Hindu by Hindus, or describe oneself perfectly validly as Hindu. One may be polytheistic or monotheistic, monistic or pantheistic, even an agnostic, humanist or atheist, and still be considered a Hindu."; [b] Lester Kurtz (Ed.), Encyclopedia of Violence, Peace and Conflict, ISBN978-0123695031, Academic Press, 2008; [c] MK Gandhi, The Essence of Hinduism, Editor: VB Kher, Navajivan Publishing, see page 3; According to Gandhi, "a man may not believe in God and still call himself a Hindu."
^"Polytheism". Encyclopædia Britannica. Encyclopædia Britannica Online. 2007. Retrieved 2007-07-05.
^Bruce Trigger (2003), Understanding Early Civilizations: A Comparative Study, Cambridge University Press, ISBN978-0521822459, pages 473-474
^Charles Taliaferro and Elsa J. Marty (2010), A Dictionary of Philosophy of Religion, Bloomsbury Academic, ISBN978-1441111975, pages 98-99
^Eric Ackroyd (2009). Divinity in Things: Religion Without Myth. Sussex Academic Press. p. 78. ISBN978-1-84519-333-1., Quote: "The jealous God who says, "Thou shalt have no other gods but me" belongs to the Jewish-Christian-Muslim tradition, but not to the Hindu tradition, which tolerates all gods but is not a monotheism, monism, yes, but not monotheism."
^Guy Beck (2005), Alternative Krishnas: Regional and Vernacular Variations on a Hindu Deity, State University of New York Press, ISBN978-0791464151, page 169 note 11
^Bruce Trigger (2003), Understanding Early Civilizations: A Comparative Study, Cambridge University Press, ISBN978-0521822459, pages 441-442, Quote: [Historically...] people perceived far fewer differences between themselves and the gods than the adherents of modern monotheistic religions. Deities were not thought to be omniscient or omnipotent and were rarely believed to be changeless or eternal."
^Bhagawan Swaminarayan bicentenary commemoration volume, 1781-1981. p. 154: ...Shri Vallabhacharya [and] Shri Swaminarayan... Both of them designate the highest reality as Krishna, who is both the highest avatara and also the source of other avataras. To quote R. Kaladhar Bhatt in this context. "In this transcendental devotieon (Nirguna Bhakti), the sole Deity and only" is Krishna. New Dimensions in Vedanta Philosophy - Page 154, Sahajānanda, Vedanta. 1981
^Flood, Gavin D. (1996). An introduction to Hinduism. Cambridge, UK: Cambridge University Press. p. 341. ISBN978-0-521-43878-0. Retrieved 2008-04-21. gavin flood."Early Vaishnava worship focuses on three deities who become fused together, namely Vasudeva-Krishna, Krishna-Gopala and Narayana, who in turn all become identified with Vishnu. Put simply, Vasudeva-Krishna and Krishna-Gopala were worshiped by groups generally referred to as Bhagavatas, while Narayana was worshipped by the Pancaratra sect."
^Knapp, S. (2005). The Heart of Hinduism: The Eastern Path to Freedom, Empowerment and Illumination -. iUniverse. "Krishna is the primeval Lord, the original Personality of Godhead, so He can expand Himself into unlimited forms with all potencies." page 161
D Hudson (1993). "Vasudeva Krsna in Theology and Architecture: A Background to Srivaisnavism". Journal of Vaisnava Studies (2).
Matchett, Freda (2000). Krsna, Lord or Avatara? the relationship between Krsna and Visnu: in the context of the Avatara myth as presented by the Harivamsa, the Visnupurana and the Bhagavatapurana. Surrey: Routledge. p. 254. ISBN978-0-7007-1281-6.