Hindu philosophy consists of six schools of thought. They are Sankhya, Yoga, Nyaya, Vaisheshika, Mimamsa and Vedanta. They are also known as the Astika (orthodox) philosophical traditions and accept the Vedas as an authoritative and important source of knowledge.
Sankhya philosophy offers a framework for all the levels of manifestation, from the subtlest to the grossest. Sankhya comes from Samyag Akhyate, which literally means that which explains the whole. Sankhya deals with matter, consciousness, intelligence, arrogance, mind, cognitive and active senses, and the five elements (earth, water, fire, air, and space).
Yoga deals with one's hunger for experiencing the eternal centre of consciousness. Yoga is best described in the Yoga Sutras. It involves a systematic witnessing of your inner states, so as to go beyond all of them to the centre of consciousness.
The Nyaya school of thought was founded by sage Gautama. It mainly teaches one to deal with logic, to use the process of reasoning. Doubt is considered a prerequisite for philosophical inquiry. A lot of other systems of Indian philosophy draw on this process.
The Vaisheshika system was formulated by Prashastapada. It stresses on the physical sciences such as chemistry. It includes exploring the elements of earth, water, fire, air, and space, as well as time, mind and soul.
Mimasa pursues freedom through action. It was founded by Jaimini. It is a detailed philosophy related to rituals, worship, and ethical conduct, which developed into the philosophy of karma.
The last school of thought is the Vedanta. The term veda means knowledge and anta means the end. The vedas are the earliest sacred literature in India and the word means the conclusion of the vedas. There are three fundamental Vedanta texts. The first one is called Upanishads, then comes the Brahma-sutras, are very brief interpretations of the Upanishads; and finally, comes the Bhagavadgita.