1. Nyaya-Vaisheshika (Logic and Atomism):

This school emphasizes logic and inference, and believes that knowledge is obtained through perception, inference, comparison, and testimony. Nyaya focuses on epistemology, while Vaisheshika expounds upon metaphysics and atomism.

Example: The Nyaya school developed a system of logic and reasoning, which is known for its detailed analysis of different types of logical inferences.

2. Samkhya-Yoga (Dualism and Yoga):

Samkhya explains the nature of the universe through the theory of dualism, distinguishing between matter (prakriti) and consciousness (purusha). Yoga complements Samkhya by offering techniques for self-realization and attaining union with the divine.

Example: The Samkhya philosophy describes the universe as a result of the interplay between the fundamental principles of prakriti and purusha.

3. Vedanta (Non-dualism):

Vedanta, derived from the Vedas, is a school that emphasizes the non-dual nature of reality. It teaches that the ultimate reality (Brahman) and individual selves (Atman) are essentially the same.

Example: Advaita Vedanta, a prominent branch of Vedanta, was founded by Adi Shankaracharya and is known for its doctrine of non-dualism, affirming that Brahman is the only reality.

4. Mimamsa (Orthodox Hermeneutics):

The Mimamsa school focuses on the interpretation and ritual application of the Vedas. It envisions a world governed by ritual duties and aims to understand the nature of rituals (karma) and their significance.

Example: Mimamsa philosophers analyze the ritualistic texts of the Vedas and provide guidelines for conducting rituals and interpreting their meaning.

5. Vaishnavism, Shaivism, and Shaktism (Bhakti and Devotion):

These philosophical schools are centered around devotion to a particular deity—Vishnu, Shiva, and the divine feminine energy (Shakti) respectively. They emphasize devotion, worship, and ritualistic practices as means to attain spiritual liberation.

Example: Vaishnavism reveres Lord Vishnu and his avatars such as Lord Krishna and Lord Rama, while Shaivism focuses on Lord Shiva as the supreme being. Shaktism worships various forms of the goddess, including Durga and Kali.

6. Jainism (Ahimsa and Non-attachment):

Jain philosophy revolves around the idea of non-violence (ahimsa) and non-attachment to worldly possessions. It emphasizes the existence of infinite souls and the potential for every individual to attain liberation (moksha).

Example: Jainism teaches the practice of non-violence not only towards human beings but also towards all living beings, promoting compassion and respect for life.

7. Buddhism (Middle Way):

Buddhism, founded by Gautama Buddha, focuses on the Middle Way—avoiding both extreme asceticism and indulgence. It teaches the Four Noble Truths as a means to overcome suffering and attain enlightenment (nirvana).

Example: One of the core teachings of Buddhism is the concept of impermanence (anicca), highlighting that all conditioned phenomena are subject to change.