The six orthodox (astika) schools of Hindu philosophy are classical philosophical traditions that accept the authority of the Vedas and acknowledge the existence of a supreme reality (Brahman).

The Shad-Darshanas, also known as the six classical schools of Indian philosophy, provide diverse perspectives on understanding the nature of reality, the self, and the means to attain liberation (moksh). These schools represent distinct philosophical systems that have played significant roles in shaping Hindu thought and culture. These schools offer different perspectives on metaphysics, epistemology, ethics, and the nature of reality. The six orthodox schools are:

1. Nyaya: Founded by sage Gautama, Nyaya is a school that focuses on logic (tarka), epistemology (pramana), and analysis of reasoning. It systematizes methods of logical reasoning and investigates the nature of knowledge. Nyaya is known for its detailed discussions on epistemological categories and logical analysis.
2. Vaisesika: Attributed to sage Kanada, the Vaisesika school explores metaphysics and atomistic philosophy. It categorizes the world into different substances and analyzes the nature of reality through the concept of atoms (anu) and their combinations.
3. Samkhya: Attributed to sage Kapil, Samkhya is a dualistic philosophy that analyzes the nature of reality through the categories of purusha (consciousness) and prakriti (matter). Samkhya enumerates the components of the universe and provides a systematic understanding of creation and liberation.
4. Yoga: Often associated with the sage Patanjali, the Yoga school builds on the metaphysical framework of Samkhya. It emphasizes the practical aspects of spiritual discipline, including ethical guidelines, physical postures (asans), breath control (pranayam), and meditation, all aimed at achieving mental and spiritual liberation.
5. Mimamsa: Also known as Purva Mimamsa, this school, attributed to sage Jaimini, focuses on the interpretation of the Vedas and rituals (karma-kanda). Mimamsa is concerned with the proper performance of Vedic rituals and the understanding of the sacrificial ceremonies described in the Vedas.
6. Vedanta: Vedanta, also known as Uttara Mimamsa, is one of the most influential schools of Hindu philosophy. It interprets the concluding portions of the Vedas (Upanishads) and addresses metaphysical questions about the nature of ultimate reality (Brahman), the self (Atman), and the relationship between the individual and the divine. There are different sub-schools within Vedanta, including Advaita (non-dualism), Visishtadvaita (qualified non-dualism), and Dvaita (dualism).

Each of these six orthodox schools offers a unique perspective on the nature of reality, knowledge, and the path to spiritual realization. While they share a common acceptance of the Vedas as authoritative scriptures, they differ in their approaches, emphasis, and conclusions regarding various philosophical matters. These schools have contributed significantly to the rich tapestry of Hindu philosophical thought throughout the centuries.