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Philosophy Schools

Classical Indian philosophy can be roughly categorized into "orthodox" (Astika) schools of Hindu philosophy, and "heterodox" (Nāstika) schools that do not accept the authorities of the Vedas.

Orthodox Schools (Astika)

Many Hindu intellectual traditions were codified during the medieval period of Brahmanic-Sanskritic scholasticism into a standard list of six orthodox (astika) schools (darshanas), the "Six Philosophies" all of which cite Vedic authority as their source:

Nyaya, the school of logic
Vaisheshika, the atomist school
Samkhya, the enumeration school
Yoga, the school of Patanjali (which assumes the metaphysics of Samkhya)
Purva Mimamsa (or simply Mimamsa), the tradition of Vedic exegesis, with emphasis on Vedic ritual
Vedanta (also called Uttara Mimamsa), the Upanishadic tradition, with emphasis on Vedic philosophy.

These are often coupled into three groups for both historical and conceptual reasons: Nyaya-Vaishesika, Samkhya-Yoga, and Mimamsa-Vedanta.

Heterodox schools (Nastika).

The schools that do not accept the authority of the Vedas are by definition Unorthodox or Heterodox (Nastika) systems.

Cārvāka - Cārvāka is characterized as a materialism and atheistic school of thought. While this branch of Indian philosophy is not considered to be part of the six orthodox schools of Hinduism, it is noteworthy as evidence of a materialistic movement within Hinduism.
Buddhist philosophy - Buddhist philosophy is a system of beliefs based on the teachings of Siddhartha Gautama, an Indian prince later known as the Buddha. Buddhism is a non-theistic philosophy, one whose tenets are not especially concerned with the existence or nonexistence of a God or gods.
Jain philosophy - The Jaina philosophy was already in existence by 6th Century BCE, when it was revived by Mahavira (599–527 BCE) the 24th Jain Tirthankar. One of the main characteristics of Jain belief is the emphasis on the immediate consequences of one's psychic behavior.

Gautama Buddha

Mahavira

Cārvāka - Cārvāka is characterized as a materialism and atheistic school of thought. While this branch of Indian philosophy is not considered to be part of the six orthodox schools of Hinduism, it is noteworthy as evidence of a materialistic movement within Hinduism.

Buddhist philosophy - Buddhist philosophy is a system of beliefs based on the teachings of Siddhartha Gautama, an Indian prince later known as the Buddha. Buddhism is a non-theistic philosophy, one whose tenets are not especially concerned with the existence or nonexistence of a God or gods.