Two kinds of Atheism:
(i) Astika Atheism:
The Sanskrit term Astika ("pious, orthodox") is sometimes translated as "theist" and Nastika as "atheist". Sanskrit asti means "there is", and Astika per Panini 4.2.60 is derived from the verb, meaning "one who says 'asti', one who believes in the existence God). When used as a technical term in Hindu philosophy the term Astika refers to belief in the Vedas, not belief in the existence of God.
There are six schools of thought within Hinduism addressed as the Shat (Astik) Darshana (darshana meaning "viewpoint."). Within the Astika schools of Hindu philosophy, the Samkhya (Kapila's system) and the early Mimamsa school did not accept a God in their respective systems.
The atheistic viewpoint as present in the Samkhya and Mimamsa schools of Hindu philosophy takes the form of rejecting a creator-God. The Samkhya school believed in a dual existence of Prakriti ("nature") and Purusha ("spirit") and had no place for an Ishvara ("God") in its system. The early Mimamsakas believed in a adrishta ("unseen") that was the result of performing karmas ("works") and saw no need for an Ishvara in their system. Mimamsa, as a philosophy, deals exclusively with karma and thus is sometimes called Karma-Mimamsa. The karmas dealt with in Mimamsa concern the performance of Yajnas ("sacrifices to gods") enjoined in the Vedas.
(ii) Nastika Atheism:
In Hindu philosophy, three schools of thought are commonly referred to as Nastika: Jainism, Buddhism and Carvaka for rejecting the doctrine of Vedas. In this usage, Nastika refers to the non-belief of Vedas rather than non-belief of God. However, all these schools also rejected a notion of a creationist god and so the word Nastika became strongly associated with them.
Carvaka, an atheistic school of Indian philosophy, traces its origins to 600 BCE, while some claim earlier references to such positions.It was a hedonistic school of thought, advocating that there is no afterlife. Carvaka philosophy appears to have died out some time after 1400 CE.