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Ancient India philosophy
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Indian philosophies share many concepts such as dharma, karma, samsara, reincarnation, dukkha, renunciation, meditation, with almost all of them focussing on the ultimate goal of liberation of the individual through diverse range of spiritual practices (moksha, nirvana).They differ in their assumptions about the nature of existence as well as the specifics of the path to the ultimate liberation, resulting in numerous schools that disagreed with each other. Their ancient doctrines span the diverse range of philosophies found in other ancient cultures.
Many Hindu intellectual traditions were classified during the medieval period of Brahmanic-Sanskritic scholasticism into a standard list of six orthodox (Astika) schools (darshanas), the "Six Philosophies" (ṣaḍ-darśana), all of which accept the testimony of the Vedas.
Samkhya, the rationalism school with dualism and atheistic themes
Yoga, a school similar to Samkhya but accepts personally defined theistic themes
Nyaya, the realism school emphasizing analytics and logic
Vaisheshika, the naturalism school with atomistic themes and related to the Nyaya school
Purva Mimamsa (or simply Mimamsa), the ritualism school with Vedic exegesis and philology emphasis,and
Vedanta (also called Uttara Mimamsa), the Upanishadic tradition, with many sub-schools ranging from dualism to nondualism.
These are often coupled into three groups for both historical and conceptual reasons: Nyaya-Vaishesika, Samkhya-Yoga, and Mimamsa-Vedanta. The Vedanta school is further divided into six sub-schools: Advaita (monism/nondualism), also includes the concept of Ajativada, Visishtadvaita (monism of the qualified whole), Dvaita (dualism), Dvaitadvaita (dualism-nondualism), Suddhadvaita, and Achintya Bheda Abheda schools.
Besides these schools Mādhava Vidyāraṇya also includes the following of the aforementioned theistic philosophies based on the Agamas and Tantras:
Pasupata, school of Shaivism by Nakulisa
Saiva, the theistic Sankhya school
Pratyabhijña, the recognitive school
Raseśvara, the mercurial school
Pāṇini Darśana, the grammarian school (which clarifies the theory of Sphoṭa)
The systems mentioned here are not the only orthodox systems, they are the chief ones, and there are other orthodox schools. These systems, accept the authority of Vedas and are regarded as orthodox (astika) schools of Hindu philosophy; besides these, schools that do not accept the authority of the Vedas are heterodox (nastika) systems such as Buddhism, Jainism, Ajivika and Cārvāka. This orthodox-heterodox terminology is a construct of Western languages, and lacks scholarly roots in Sanskrit. According to Andrew Nicholson, there have been various heresiological translations of Āstika and Nāstika in 20th century literature on Indian philosophies, but quite many are unsophisticated and flawed.
Cārvāka / Charvaka is a materialistic and atheistic school of thought and, is noteworthy as evidence of a materialistic movement within Hinduism.