4.Yoga Darshana
Yoga is that which helps a jiva to attain  concentration on Ishwara and ultimate union with Him. Sage Patanjali’s work entitled the Yoga Sutras is the extremely  influential text for this school of thought.

Samkhyan doctrine of the relationship between Purusha  and Prakriti is crucial to Patanjali's Yoga Darshana. The Samkhya system  accepts only purusha, the individual soul and prakrti or pradhana, the nature  or matter as the fundamental realities and does not accept Ishwara or God. The  Yoga Darshana accepts all the principles of the Samkhya and Ishwara or God, in  addition.  The Samkhya gives primary  importance to tattwajnana or enquiry  into the nature of truth while the Yoga deals primarily with sadhanas or spiritual disciplines.

The significant variation of the Yoga from the Samkhya  is not only the incorporation of the concept of Ishvara (a personal God) into its  metaphysical worldview (which the Samkhya does not) but also upholding of  Ishvara as the ideal upon which to meditate.
It also utilizes the Brahman/Atman terminology and concepts that are  found in the Upanishads, thus  breaking from the Samkhya school by adopting concepts of Vedantic nondualism.

The Yoga system lays down elaborate prescriptions for  gradually gaining physical and mental control and mastery over the  "personal self", both body and mind, until one's consciousness has  intensified sufficiently enough to allow for the awareness of one's "real  Self" (the soul, or Atman), as distinct from one's feelings, thoughts and  actions. By following these prescriptions or sadhanas (ashtanga yoga or eight  steps of yoga) one realises his essential nature and instantly freed from  samsara, the cycle of transmigration, and attains kaivalya.

Realization of this goal of Yoga is known as moksha, nirvana and samadhi. This realization of the Atman is nothing  other than attaining the infinite Brahman.

5. Purva Mimamsa  Darshana
The  main objective of the Purva (earlier) Mimamsa  school was to establish the authority of the Vedas.  Consequently this school's most valuable contribution to Hinduism was its formulation of the methodology of  interpretation with the help of which complicated Vedic injunctions regarding  rituals are understood and practised. The mimamsa  sutras of Jaimini is the basic text of this system.

Its  adherents (Mimamsakas) believed that -
  1.  One must have unquestionable faith in the Vedas which are infallible.
  2.  There is a soul which survives the death of the body and enjoys the fruits of  the rituals in heaven.
  3.  There is a power of potency which preserves the effects of the rituals  performed in the soul yielding fruits after death.
  4.  The world is real.
  5.  Our life and actions performed here are real and not mere dreams. 

They  believe in a magical power of the mantras and yajñas which sustains all the activity of the  universe. In keeping with this belief, they laid great emphasis on dharma, which they understood as the  performance of Vedic rituals. Every human being is bound to perform these Vedic  duties for duty’s sake only because Vedas command them and none has got the  choice not to do them or do them in a different way.

The Mimamsa accepted the logical  and philosophical teachings of the other schools, but felt that they paid  insufficient attention to right action. According to the Mimamsa, the very  striving for liberation stemmed from a selfish desire to be free. Only by  acting in accordance with the prescriptions of the Vedas could one attain salvation  which includes a belief in the varna and ashrama system.

While Mimamsa does not receive  much scholarly attention these days, its influence can be felt in the life of  the practising Hindu in the performance of rites, rituals and observance of religious  ordinances.