What is Moksha or Mukti

Our thoughts and actions/activities are governed by desires, aversions, attachment to rewards, egotism or “I am” etc. Mind (मन) seeks favourable things to happen. In unfavourable circumstances, malice creeps in. The desires, aversions, attachment, karma etc. goes along with jeevatma (soul) in subtle body in form of samskara or impressions which manifest in future body, at the time of re-birth.
 
According to Hinduism, Dharma, Artha, Kama and Moksha are purpose or Purushartha of life. One’s journey of life is fulfilled by earning material prosperity (Artha) and enjoying it (kama) while meticulously performing religious & moral duties (Dharma) and ultimately liberating oneself through self-realisation (Moksha). Moksha is dropping and detachment of dharma, artha and kama. Awareness of causes of miseries and path of self-realisation leads to moksha. Moksha is also called Mukti or Kaivalya. However, some schools believe Moksha & Mukti are different. By following one of the four paths viz. Karma yoga, Bhakti Yoga, Raja Yoga & Jnana Yoga, one can attain Moksha.
The concepts of Mukti, Moksha, Dharma, Artha, Kama and four paths of Moksha are explained hereunder:

What is Mukti
By dissociation from desires, miseries, attachment etc and by extinguishing karma (past & present), Atma becomes free from bondages and become free and mukt. The state of such freedom is Mukti.
 
What is Moksha
Moksha is derived from the root Sanskrit: मुच्, muc, which means free, let go, release, liberate. One of the fundamentals of Hinduism is re-birth of Atma (soul). Liberation or Release of self, freedom from saṃsāra, the cycle of death and rebirth through self-realisation is Moksha.
 
Moksha is not merely absence of suffering and release from bondage to saṃsāra (worldly affairs), but attaining the state of oneness with Brahman, the One Supreme Self.

Dharma, Artha and Kama      
Dharma is living in righteous way which includes the religious duties, moral rights and duties of each individual, as well as behaviours that enable social order, right conduct, and those that are virtuous. On death, all people, money, materials, body remain here. Only dharm goes along atma. When we understand Dharma, man reflects patience, forgiveness, mental strength, - peace, purity.
Artha incorporates wealth, career, activity to make a living, financial security and economic prosperity. Arhta with Dharma is use of wealth for the well-being of others
Kama signifies desire, wish, passion, emotions, pleasure of the senses, love, with or without sexual connotations. 

Paths for Moksha

1. According to six major schools of Hindu philosophy, Jeevatma get liberated when it becomes free from sin, sorrow, hunger, thirst, desires, volitions etc. and attain pure intelligence. A liberated soul is master of himself and free from re-birth. (Ref. Vedanta Sutra – 4.4.5, 4.4.22, 3.4.27; Nyaya – 1.1.22, 4.2.41, 4.2.45; Vaisheshik – 5.2.18, 6.2.2; Samkhya – 1.1, 1.1.24, 6.17, 6.26; Yog – 4.34; Mimansa – 6.2.19).
2. The Nyaya, Vaisesika and Mimamsa schools of Hinduism consider moksha as possible only after death. Samkhya and Yoga schools consider moksha as possible in this life.
3. In Samkhya school, Moksha is referred as Kaivalya i.e. realisation of purusa or consciousness, by attaining wisdom. This is called Jnana yoga or Marga.   
4. In Yoga school, the eight limbs of yoga lead to Samadhi, a state of awareness & bliss and oneness with purusha (atma) also called Kaivalya. The practice of the eight limbs of yoga with detachment (vairāgya), which over time leads to deep concentration (samādhi). This is called Raja Yoga or Marga.
5. In Vedanta school, the Advaita sub-school concludes moksha is possible in this life through Janan (wisdom). (Jnana Marga)
6. In Vedanta school, Dvaita and Visistadvaita sub-schools believe that moksha is possible by bhakti or devotion to God (without any other thought) that extends from this life to post-mortem. This is Bhakti Marga.
7. Sri Krishna explained Arjuna in Bhagwat Geeta that nobody can remain without doing some activity. The activity done in expectation of particular reward brings attachment. The result brings pleasure or pain. If activity is done without attachment (nishkam karma) whatever result comes, it will not disturb the mind. While performing worldly duties or karma, detachment avoid pains. Our five senses (touch, taste, seeing, hearing and smell) are manipulated by external influences which create desires and mind decides to do certain activity for sensual pleasure. Whereas when assigned karma done without bias and expectation of rewards but dedicated true self (Atma), one attain liberation or state of bliss. This is Karma yoga or marga. 

 
Reference:

1. Shad Darshanam, Swami Jagdishwaranand Saraswati,  Publisher: Vijaykumar Govindram Hasanand, 4408, Nai Sarak, Delhi – 110006.

1. https://en.wikipedia.org/wiki/Moksha
2. https://en.wikipedia.org/wiki/Purusartha