Between sixth century B.C at the time of Asoka. The Darsanas are given in the form utras or aphorisms which are short short definite and free from doubt. The Darsanas are given in the form of sutras consist the ideas of Avidya,Maya,Purusha and Jiva are common in all philosophy. They all protest against the scepticism of the Buddhists and erect or raise "a standard of objective reality and truth as opposed to eternal and Nirvana , unstable flux." They all believe in the creation, maintenance and dissolution of the world. Excepting the purva Mimansa, the other system aim at Moksha or the release of the soul from rebirths and gain immortal peace . It is pointed out that the way to attain Moksha is through Chittasuddhi or purification of mind out that way to attain Moksha is through Chittasuddhi or purification of mind and NIshkam Karma or disinterested activity.
1) Nyaya Philosophy: It is given by Gautam Rishi. According to it , Tarka is the basis of all studies. It is the science of sciences. Knowledge can be acquired by four metho are Pratyaksha or intuition, Anumana or inference, Upma or comparison and Sabda or verbal testimony.Anumana is of three kinds, viz, Purvavat,Sesavat and ascribes it to the lapse of memory or irregularities or aberrations in recognition or perception of the daily life. Error is the apprehension of an object other than what it actually is or we called false. Truth reveals itself to those who have experience(satya). The soul is real,truth and its attributes are desires,aversions,voilitions, etc. Consciousness cannot exist apart from the soul"as the brilliance of flame cannot live apart from it" it's truth. The Nyaya Darsana believes in God who is full of knowledge and bliss and superpower. The theory of rebirth is accepted and the people are asked to release themselves from its bondage and free from earthly life.
2)Kanada Rishi is the the author of the Vaisesika Darsana and it is solely concerned with the padarthas which are divided into six categories: Dravya or substance,Guna or quality, Karma or activity ,Samanya or generality,Visesha or particularity and Samavaya or eerence. The nine dravyas(element) or substances are earth,water,air,light,Akasha, time ,space, soul and Manas. Atoms are the ultimate constituents of concrete things. Atoms cannot be destroyed . All that happens is that they take a different shape in life. There are 17 kinds of qualities. Karma or activity is transient and comes to an end at one stage or the other stage of life. Kanada does not make any direct reference to God almighty. His philosophy is not a complete philosophy of the Universe.
3) Kapila was the author of the sankhya Darsana. Its fundamental principle and idea is the dualism of Purusha and Prakriti. Prakriti is developed by three kinds of gunas viz,Sattva Guna(HEAVENLY),Raja Guna(EARTHLY) and Tamas Guna(HELL). Sattva Guna is the source of good and happiness in life. Rajas Guna is the source of activity and pain(earthy). Tamas Guna is the source of ignorance, sloth and apathy and distress. The world is not regarded as real. It is not real in the sense that it doesn't exist for ever and after some time it is destroyed. The only thing that is eternal is prakriti. While the purusha is external, the jivas are bound by the bondage of rebirth. The sankhya Darsana does believe in the existence of god and mythodology. Prakriti and purusha are independent and not dependent upon God or idle.
4) Patanjali was the author of the Yoga Darsana. A person can be liberated from the circle of rebirths by the practice of Yoga or the concentration of mind repeatedly. Efforts should be made to developed both the physical and spiritual sides of life. Eight methods have been suggested in the Holy Process to achieve the objective and those are Yama or adstention, Niyama or observance, Asana or posture, Pranayama or regulation of breath, Pratyahara or withdrawal of the senses, Dhyana or fixed attention and samadhi or concentration. By the pratice of Hatha Yoga,body can be brought under the control and made capable of bearing great strains. The control of the breath has a great steadying influence on the mind. The Yoga ends in Dhyan and samadhi.When a man achieves the stage of samadhi, he loses his corned in with the world,God alone is the object of meditation and he alone helps us to attain our goal.
5)Jaimini was the author of the Purva-Mimansa Darsana. It is They concerned with rituals, authority of Vedas is accepted. The self is different from the body , sense and understanding.The plurality of souls is also recognized.Dharma is the scheme of right living. There are two kinds of functions and those are Nitya Karma(daily practice) and the Kamya Karma(seek of boon). The one is done everyday regularly  and the other is done to achieve some special object for fortune.Offerings should be made to a number of deities for boon . There is no necessity of a benevolent or active God as i mention. The Purva Mimansa Darsana is concerned with purely mechanical ethics and doesn't attack the problems of ultimately reality. Its concerned only with Karmakand or the performance of sacrifices.
6) Badarayana was the author of Uttar Mimansa Darsana wrote 55Sutras which are divided into four chapters. The first chapter deals with the nature of Brahmana and his relation with the world and the individual souls. The second deals with the objections. The third discusses the ways and means of attaining Brahma Vidya. The fourth deals with the fruits of brahma Vidya and the future of soul after death.