At least three kinds of visions of God have arisen in the Hindu world.
Visualizable Representations. God as the Supreme principle has a triple aspect, each bearing a name: Brahma (Creator), Vishnu (Sustainer); and Shiva (Dissolver), and their consorts Sarasvati (Goddess of Learning), Lakshmi (Goddess of Prosperity), and Uma (Mountain Goddess).
Epic Personages. Certain heroes in major Hindu epics are regarded as manifestations of the Divine in human form. They are said to have appeared on earth during other eras (yugas) of human history. The most important of them are Rama, Krishna, and Murugan (among the Tamils of the south).
Abstract Principle. Divinity is also associated with an immanent principle that transcends human understanding and description, called Brahman. Brahman is abstract divinity beyond visualization and logical categories whose existence can be confirmed and experienced by the human spirit through spiritual exercises and self-surrendering devotion.
The Hindu concept of the Divine may be explained through an analogy: Consider a sumptuous dinner that you are enjoying through your perceptual channels of taste. The dinner became possible because of the cooking, which involves cutting the vegetables, boiling, frying, adding the right amounts of spices, etc. If these do not occur in precise and well-defined ways, the food will not appear in its delectable form. Finally, beyond the cooking and resulting products, there is the essence of the food itself: the proteins, the carbohydrates, the vitamins, the minerals, etc. These lie hidden from our normal view. Ultimately, it is the life-fueling energy implicit in the food that is responsible for our health and well-being. This energy is all too abstract to be visualized in its stark purity. It finds expression through a hundred different biochemical molecules. Thus there are three distinct dimensions of the food: the perceived level, the processes engendering it, and the basic invisible level, which is the ultimate source of it all.
According to the Hindu worldview, in the course of our everyday experience we become aware of things and events. A characteristic of all tangible constituents of the universe, whether of any life form or even of inanimate entities is transience: Sooner or later everything in the world transforms and dissolves. This transient dimension of the world is called kshara: that which is destructible. The perceptible universe consists of all these transient things.
Underlying the tangible material universe are immutable fundamental physical laws that are responsible for the functioning of the perceived world. These laws are not directly visible to us, but their nature and complexity can be grasped by the human mind. In the Hindu framework, the totality of natural laws is known as the akshara, or unerasable dimension. It gives rise to the kshara.
In the Hindu religious worldview, beyond the empirical and the intellectually grasped features, there is a third dimension. This is the ultimate substratum of the universe, somewhat like the essence of the food. It is recognizable neither mentally nor perceptually because it does not manifest itself in any way. It is referred to as the avyaya, or unmanifest dimension. Its existence and essence can be apprehended by human consciousness by processes that transcend the perceptual- mental modes. This apprehension is what spiritual enlightenment is all about.
This unmanifest root of the cosmos is Brahman. Brahman is the equivalent of God in the Hindu framework. Brahman is beyond the constraints of space and time, of logic and causality. That is why verbal discourses on the nature of God always lead to contradictions and confusions. Brahman is to be apprehended, not comprehended; experienced, not described; vouched for, not proved. Those who have realized Brahman speak of ecstasy and bliss, not of belief or faith.
The material representations of the God symbols are called murtis, inappropriately referred to as idols by outsiders. A murti is a mapping on the visual plane of a transcendent principle that is too subtle for ordinary minds to grasp. It is not unlike a geometrical figure that a mathematician may draw to reach a result that he cannot as easily derive through reasoning alone. The murti enables the practitioner to engage in meaningful interactions with that for which it stands. As to the question whether Hinduism is monotheistic or polytheistic, the answer would be: "There is but one God, and there are also many."
Again, to clarify the Hindu concept, an analogy may be considered. It is difficult to intellectually grasp what music is: Music is to be experienced, not defined. Is there one music or many? "Music" represents one entity, but its expressions are countless. Most people know "music" through its many expressions such as songs, sonatas, etc. Very few understand "music" at the intellectual and abstract level. They enjoy particular musical pieces and expressions and have no need to define it.
This, roughly, is the Hindu view of god. Like "music," there is one universal God, but, like "music," that God can only be experienced through one or more of the multiple manifestations.