Gautama is considered the founder of the Nyaya school of philosophy, while Kanada is considered the founder of the Vaiseshika school of philosophy. The two schools were later combined to form the Nyaya-Vaiseshika school of philosophy.

The Nyaya-Vaiseshika school of philosophy is known for its emphasis on logic and epistemology. It is one of the few schools of Indian philosophy that has a developed system of logic.

Pramana is the Nyaya-Vaiseshika school's theory of knowledge. It is a system of epistemology that seeks to determine the sources and validity of knowledge.

The Nyaya-Vaiseshika school of philosophy recognizes four pramanas, or sources of knowledge: perception, inference, comparison, and testimony.

Anumana is the Nyaya-Vaiseshika school's theory of inference. It is a system of logic that seeks to determine the validity of inferences.

Padartha is the Nyaya-Vaiseshika school's theory of categories. It is a system of metaphysics that seeks to identify and classify the different types of entities that exist in the world.

The Nyaya-Vaiseshika school of philosophy recognizes seven padarthas, or categories: substance, quality, action, generality, particularity, inherence, and non-existence.

Paramanu is the Nyaya-Vaiseshika school's theory of atomism. It is a system of metaphysics that seeks to explain the nature of matter and the universe.

Moksha is the Nyaya-Vaiseshika school's theory of liberation. It is a state of liberation from the cycle of birth and rebirth.

The Nyaya Sutras are considered to be the most important work of the Nyaya-Vaiseshika school of philosophy. They were written by Gautama and contain the school's basic principles.

Vatsyayana is considered to be the most important commentator on the Nyaya Sutras. He wrote a commentary called the Nyaya-Bhasya, which is considered to be one of the most important works of the Nyaya-Vaiseshika school of philosophy.

Samavaya is the Nyaya-Vaiseshika school's theory of universals. It is a system of metaphysics that seeks to explain the relationship between universals and particulars.

Karyakara is the Nyaya-Vaiseshika school's theory of causation. It is a system of metaphysics that seeks to explain the relationship between cause and effect.

Kala is the Nyaya-Vaiseshika school's theory of time. It is a system of metaphysics that seeks to explain the nature of time.

Dik is the Nyaya-Vaiseshika school's theory of space. It is a system of metaphysics that seeks to explain the nature of space.