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The term Rishi (Sanskrit: ṛṣi, Devanagari: ऋषि) originates from the ancient pre-Hindu culture of the Indus region earth-based cultures. Rishis were the scribes of the large body of nature hymns and spiritual science known as the Vedas.
A Rishi (or rishika, when referring to female rishis) is a sage of insight, one who practices self-cultivation as a Yogini or Yogi and attains asamprajñata Samadhi. A person through Yogic concentration first attains samprajñata samadhi (realisation of the independence of soul and body, Atma and Prakriti) and with continued effort attains asamprajñata samadhi (realisation of oneness with all). The Rishi's soul is interpreted as imbibing wisdom directly from the universal source. Vedic hymns are sermons conceived as delivered by divine inspiration by the rishis.
According to the term in popular culture, a Rishi will never contradict another Rishi due to their knowledge being directly revealed from God.
According to Indian tradition, the word was derived from the two meanings of the root rsh. Sanskrit grammarians derive this word from the second root which means "to go, to move". gives this particular meaning and derivation, and Monier-Williams also gives the same, with some qualification.
Another form of this root means (2) "to flow, to move near by flowing". (All the meanings and derivations cited above are based upon Sanskrit English Dictionary of Monier-Williams). Monier-Williams also quotes Tārānātha who compiled the great (Sanskrit-to-Sanskrit) dictionary named "ṛṣati jñānena saṃsāra-pāram" (i.e., "one who reaches beyond this mundane world by means of spiritual knowledge").
More than a century ago, Monier-Williams tentatively suggested a derivation from drś "to see". Monier-Wiliams also quotes the Hibernian (Irish) form arsan (a sage, a man old in wisdom) and arrach (old, ancient, aged) as related to rishi. In Sanskrit, forms of the root rish become arsh- in many words, (e.g., arsh. Monier-Williams also conjectures that the root drish (to see) might have given rise to an obsolete root rish meaning "to see".
However, the root has a close Avestan cognate ərəšiš "an ecstatic" (see also Yurodivy, Vates). Yet, the Indo-European dictionary of Julius Pokorny connects the word to a PIE root *h3er-s meaning "rise, protrude", in the sense of "excellent, egregious".
Modern etymological explanations such as by Manfred Mayrhofer in his Etymological Dictionary leave the case open, and do not prefer a connection to ṛṣ "pour, flow" (PIE *h1ers), rather one with German rasen "to be ecstatic, be in a different state of mind" (and perhaps Lithuanian aršus).
Other uses 
In Carnatic Music, "Rishi" is the seventh chakra (group) of Melakarta ragas. The names of chakras are based on the numbers associated with each name. In this case, there are seven rishis and hence the 7th chakra is "Rishi".
The descendent families of these Rishis, refer to their ancestral lineage through their family "gotra". This is a common practice among the Brahmin sects of the current Hindu society.
"Seer" of the Vedas 
In the Vedas, the word denotes an inspired poet of Ṛgvedic hymns, who alone or with others invokes the deities with poetry. In particular, Ṛṣi refers to the authors of the hymns of the Rigveda. Post-Vedic tradition regards the Rishis as "sages" or saints, constituting a peculiar class of divine human beings in the early mythical system, as distinct from Asuras, Devas and mortal men.
Seven Rishis (the Saptarshi) are often mentioned in the Brahmanas and later works as typical representatives of the pre-historic or mythical period; in Shatapatha Brahmana 184.108.40.206 (Brhad Aranyaka Upanisad), their names are Uddālaka Āruni (also called Gautama), Bharadvaja, Vishvamitra, Jamadagni, Vashista, Kashyapa, and Atri. Daksha, Bhrigu and Nārada were also added to the saptarshis riṣis in Āshvalāyana-Shrauta-Sutra, where these ten principals were created by the first Manu (Svāyambhuva Manu) for producing everyone else.
The notable female rishikas who contributed to the composition of the Vedic scriptures are: The Rig Veda mentions Romasha, Lopamudra, Apala, Kadru, Visvavara, Ghosha, Juhu, Vagambhrini, Paulomi, Yami, Indrani, Savitri, and Devajami. The Sama Veda adds Nodha, Akrishtabhasha, Sikatanivavari and Gaupayana.
In Mahabharata 12, on the other hand, there is the post-Vedic list of Marici, Atri, Angiras, Pulaha, Kratu, Pulastya and Vashista. The Mahābhārata list explicitly refers to the saptarshis of the first manvantara and not to those of the present manvantara. Each manvantara had a unique set of saptarshi. In Harivamsha 417ff, the names of the Rishis of each manvantara are enumerated.
In addition to the Saptarṣi, there are other classifications of sages. In descending order of precedence, they are Brahmarshi, Maharshi, Rajarshi. Devarṣi, Paramrṣi, Shrutarṣi and Kāndarṣi are added in Manusmriti iv-94 and xi-236 and in two dramas of Kālidasa.
The Chaturvarga-Chintāmani of Hemādri puts 'riṣi' at the seventh place in the eightfold division of Brāhmanas. Amarakosha (the famous Sanskrit synonym lexicon compiled by Amarasimha) mentions seven types of riṣis : Shrutarshi, Kāndarshi, Paramarshi, Maharshi, Rājarshi, Brahmarshi and Devarshi. Amarakosha strictly distinguishes Rishi from other types of sages, such as sanyāsi, bhikṣu, parivrājaka, tapasvi, muni, brahmachāri, yati, etc.
Other uses 
Rishi is also a male given name.
See also 
- cf. Commentary on Unādi-Sutra, iv, 119
- Dhātupāṭha of Pānini, xxviii). V. S. Apte
- V. S. Apte (Sanskrit-Hindi Kosh, 1890, reprint 1997 by Motilāl Banārasidās Publishers, Delhi)
- Monier-Williams, Monier (1899), A Sanskrit-English Dictionary, Delhi: Motilal Banarsidass, p. 226
- Yasna 31.5; cf. 40.4
- Etymologisches Wörterbuch des Altindoarischen, Heidelberg 1986, I 261
- South Indian Music Book III, by Prof. P Sambamoorthy, Published 1973, The Indian Music Publishing House
- Ragas in Carnatic music by Dr. S. Bhagyalekshmy, Pub. 1990, CBH Publications
- Amarakosha (2.7.41–42)
- e. g. RV 10.82.2 and 10.109.4 ; AV 60.40.1.
- Apte, Vaman Shivram (1965), The Practical Sanskrit-English Dictionary (Fourth Revised and Enlarged ed.), New Delhi: Motilal Banarsidass, ISBN 81-208-0567-4
- Apte, Vaman Shivram (1966), Sanskrit-Hindi Koṣa (Reprint 1997 ed.), New Delhi: Motilal Banarsidass
- Chopra, Deepak (2006), Life After Death: The Burden of Proof (first ed.), Boston: Harmony Books
- Kosambi, D. D. (1956), An Introduction to the Study of Indian History (Second ed.), Bombay: Popular Prakashan Pvt Ltd, 35c Tardeo Road, Popular Press Bldg, Bombay-400034
- Śāstri, Hargovind (1978), Amarkoṣa with Hindi commentary, Vārānasi: Chowkhambā Sanskrit Series Office
- The dictionary definition of rishi at Wiktionary