From the earliest Aryan periods of Hindu thought, the existence of a single supreme deity has been present. People usually credit Zoroaster or Abraham as the father of monotheism (the worship of a single God), however the Indian Vedas (Books of Knowledge) taught the doctrine long before either of the great prophets were born. As we read in the Brihadaranyaka Upanishad 3.9.1:
"Then Vidaghdha, son of Shakala, asked him, "How many gods are there, Yajnavalkya?" Yajnavalkya, ascertaining the number through a group of mantras known as the Nivid, replied, "As many as are mentioned in the Nivid of the gods: three hundred and three, and three thousand and three."
"Very good," said the son of Shakala, "and how many gods are there, Yajnavalkya?"
"Thirty-three."
"Very good, and how many gods are there, Yajnavalkya?"
"Six."
"Very good, and how many gods are there, Yajnavalkya?"
"Three."
"Very good, and how many gods are there, Yajnavalkya?"
"Two."
"Very good, and how many gods are there, Yajnavalkya?"
"One and a half."
"Very good, and how many gods are there, Yajnavalkya?"
"Ek [one]."
So, what of the other "three thousand, three hundred and five" gods (some say even more)? Here is where we find the heart of Hindu theology.
First, we must understand that Hinduism is not a single religion like Christianity, Judaism, Islam and so on, it is the composite of many different religious traditions blended together into an intended unity. These diverse religions, when taken as a group, are known as the Sanatana Dharma or Universal Truth or Way. The name "Hinduism" is a slang term that has generally been accepted as though this were a single religion. Similar to the way the Religious Society of Friends is better known as "Quakers," an originally pejorative term that they chose to embrace.
"Hindus" differ one from another in many significant respects and over the millennium the principle deities they worship have shifted and transformed as well. Today, the majority of Hindus worship "forms" or "emanations" of Vishnu/Narayana, Siva/Rudra, or Devi -- generally speaking. Practically no one worships Lord Brahma as a principle deity, although all acknowledge his role as temporal creator.
Most Hindus conceive of God in transcendence, which is to say, they readily acknowledge that the specific names and forms attributed to "God" are but limited conceptions of That Which Is Beyond Comprehension (apart from Self Realization and even then the Truth, when spoken, is clouded by illusion). God is more.
Many Hindus worship various forms of Visnu/Narayana such as Sri Krsna (Krishna) or Sri Ramacandra. They follow the teachings of scriptures such as the Mahabharata, the Srimad Bhagavad Gita (you can read my free online translation Click Here), the Ramayana and so on. They also accept all of the standard texts like the Upanishads, Puranas and so on.
Others conceive of God in forms of Lord Siva (Shivah, Rudra... and his consort Parvati), and revere scriptures such as the Tirukural (Click Here).
Others worship the Goddess (Devi) in Her various forms, as Kali, Durga, etc. and read scriptures such as the Devi Gita, the Devi Mahatmya and so on.
These of course are only the more significant divisions. Hinduism is incredibly rich and diverse.
In popular Hinduism most Hindus honor all the various deities. Families as well as individuals tend to have what are known as ista devatas or personal "house gods" that are honored. For instance, a Vaisnava worships Lord Vishnu, however at home he/she might specifically worship Lord Jagannatha due to some tradition or some specific event in the family's or individuals past. This appears like polytheism to those who do not properly understand what is being done. For Hindus however it is the honoring of specific aspects of the One.
Despite this, the concept is generally held in mind, even if it is not usually voiced, that, as the ancient Rg Veda says, "Truth is one, the sages call it by different names." or as cited above, there is only Ek Devata, the one true and utterly transcendent God, despite the seeming plurality.
For one who principally worships Lord Siva, the worship of Lord Visnu is not problematic (nor is the worship of Lord Siva for Vaisnavas). There may be some "sibling rivalry" that argues that Siva is higher than Visnu or vice versa, but in the end, Hindus believe that Truth is One.
Then there are the multitudinous demi-gods or lesser gods who act as governors in the service of the Ek Devata. They fulfill specific "functions," for instance, when beginning some new undertaking both Vaisnavas, Sivaites and worshipers of the Great Goddess will often invoke the blessings of Lord Ganapati (the elephant-headed Lord Ganesha, son of Lord Siva and Goddess Parvati).
For most Hindus, the true identity of "the ultimate God" is not what matters and is seldom discussed or even considered. No one can know Ek Devata fully. The important thing is what we might consider "spirituality" or the living of a spiritual life, and tradition. Hindus understand that God transcends all superficiality, diversities and personal preferences. Hindus therefore knowingly worship the One God in diverse forms as best suits their individual or community needs and traditions.
Then there is the arguably more philosophical side of Hinduism (inspired by the Buddha), often referred to as Vedanta, or the "End of the Vedas." Masters such as Srila Sankara (circa 800 CE) developed the Path of Impersonalism, wherein the various deities are seen metaphorically rather than as literal gods and goddesses to be worshiped.
Although Sikhism now exists as a separate religion, it did develop within a Hindu/Indian context and it is important to note the ten Sikh guru's developments here, where the One God is seen as Sound (Nam) that transcends all form and yet, unlike with the Vedantists, Sikhs continue to accept and worship an individual transcendent "God" within nirguna (hence Sikhs have altered the traditional meaning of this concept). Many Hindus accept this teaching as well. In other words, most Hindus believe in a Self-existing personal God.
Guru Nanak once visited Jagannatha Puri, one of Hinduism's four holiest mandirs or temples. As usual, he did not visit as a votary, but "to teach the people that the worship of God was superior to the worship of the deity." The high priest recognized Guru Nanak and invited him to take part in the artik or ceremony. Guru Nanak declined the honor, which outraged the priests. He replied by raising his eyes to heaven and uttering a most beautiful Sabad (divine utterance). This Sabad reflects the Sikh view of God nicely:
The sun and moon, O Lord, are Thy lamps; the firmament Thy salver; the orbs of the stars, the pearls encased in it.
The perfume of the sandal [tree] is Thine incense; the wind is Thy fan;
all the forests are Thy flowers, O Lord of light.
What worship is this, O Thou Destroyer of birth?
Unbeaten strains of ecstasy are the trumpets of Thy worship.
Thou hast a thousand eyes and yet not one eye;
Thou hast a thousand forms and yet not one form;
Thou hast a thousand pure feet and yet not one foot;
Thou hast a thousand organs of smell and yet not one organ
I am fascinated by this play of Thine.
The Light which is in everything is Thine, O Lord of Light.
From its brilliancy everything is brilliant;
By the Guru's teaching the light becometh manifest.
What pleaseth Thee is the real Arti.
O God, my mind is fascinated with Thy lotus feet as the
Bumble bee with the flower: night and day I thirst for them.
Give the water of Thy grace to the sarang note 28., Nanak, so that he may dwell in Thy name.
The One God exists in utter transcendence.
It is argued that Srila Sankara's doctrine arose in India as a reaction to Buddhism. Those who adopted this view felt that the religions of the Sanatana Dharma had developed into superstitions and vain traditions, that they had lost their spiritual potency. They blamed this development, and the perceived corruption of the Brahminical hierarchy, for the rise of the Buddhadharma (Buddhism) in India (circa 5th century BCE). That new dharma (religion) threatened to destroy traditional Hinduism and Vedantists viewed themselves as reformers and saviors of the Sanatana Dharma. This view seeks to filter out all cultural influences and achieve the distilled wisdom of the Vedas (i.e. the 'end of the Vedas') in its pure form. It remains very popular.
While the majority of religious Hindus continue to worship Ek Devata through the ancient gods and goddesses thanks to masters such as Srila Ramakrishna, Srila Vivekananda, and so many others, Vedanta has been fully incorporated into popular Hinduism, giving it a more eclectic and universal appeal than previously. Many Impersonalists, sometimes known as Mayavadis, worship murtis (deity images) but see them as symbols or holders of truth rather than as distinct or literal manifest gods/goddesses.
Rather than the heavenly "pleasure groves" of the spiritual world sought by "Personalist" Hindus, the "Impersonlists" seek a unified field of being that is practically indistinguishable from the Buddhist concept of Nirvana (for this reason, many people consider Shankaracharya a closet Buddhist, while others credit him as the savior of the Hindu dharma). My view falls somewhere in between. I hold Srila Sankara in the utmost respect.
For the personalists, the neti-neti or Not-this Not-that state of being that is achieved by this impersonalist samadhi (in "nirguna Brahman"), is but the shining effulgence of the Personality of Godhead and hence is typically accepted as a "lesser truth" or enshrouded realization.
Hence, within Hinduism, there is room for both personalist and impersonalist approaches. Monotheism, polytheism, animism and non-theism are present as well. The Sanatana Dharma is truly all-inclusive. Indeed, all religions technically belong to the "Sanatana Dharma" as all are seeking the Universal Truth!
Here is the essential difference between these two views:
Material reality is said to be "saguna". This is to say, "sa" or with and "guna" or qualities, i.e. separate existences. For personalists, upon moksa or liberation, the atman (the individual self or being or "jiva") continues to exist in the presence of God, the Paramatman ("param" highest, "atman" Self or Being). Material existence is seen as real, but temporary. Spiritual reality is understood to be real and eternal.
For impersonalists, material nature is not real but illusion (or maya). These "Mayavadis" (affirmers of the doctrine of the illusion of manifest existence) believe that upon moksa (liberation) the atman (as the falsely perceived individual self) awakens to the truth that everything is in reality non-differentiated oneness, not-this, not-that or neti-neti, and utterly beyond all duality. The material multiverse is hence deemed as merely an illusion, a dream from which the atman (embodied self) eventually awakens at liberation (as the Self realizes her true oneness with Paramatman). The jiva does not "become God" but rather realizes that everything, including "God" is but aspect-less (nirguna) Whole.
From this perspective then there are technically no gods or goddesses. "God" is not a differentiated Being from anything else. Param-atman (the individual highest Being) is but the non-differentiated totality of Awareness/Existence. Again, essentially the same as in Buddhism.
So to sum this up,
It would therefore be inaccurate to refer to this branch of Hinduism as either monotheistic or polytheistic, it is decidedly non-theistic.
Popular Hinduism appears polytheistic at times, and a few Hindus actually are, but by and large, Hindus are monotheistic, even though their conceptions are a bit different from those of Judaism, Christianity and Islam. The Ek Devata or One God of the Hindus is utterly transcendental to all description.
As Sri Krsna, beloved avatar of Sri Visnu explains:
Srimad Bhagavad Gita 10:12-15:
Arjuna said: You [Sri Krsna/Visnu] are the Supreme Brahman, the Highest Abode, the Ultimate Purifier, the Eternal Person, the Divine Primeval God, unborn and all pervading! All the seers describe You thus, including the divine rishi Narada, Asitah, Devala and Vyasa, and now You confirm it to me Yourself. I accept as truth everything You are telling me, O Keshava. O Blessed One, Your manifestations are not even understood by the devas or danavas. Oh Supreme Person, You alone know Yourself by Yourself, O Source of all beings, Master of all beings, God of gods and Ruler of the universe!
From the Svetasvatara Upanishad 6.11:
He is the Sole Supreme Being; of eternal manifestation; Creator, Immanent Reality; Without Fear, Without Rancor; Timeless Form; Un-incarnated; Self-existent; Realized by the grace of the Holy Preceptor [Guru].
