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Abbasi came with his parents to the United States and grew up in Los Angeles. Wes Montgomery, Jim Hall, Pat Metheny, and Bill Frisell were successively his musical influences on guitar. Others include John Coltrane, Keith Jarrett and many non-jazz musicians. He studied at the University of Southern California and Manhattan School of Music jazz and classical music, then he went to India, where he learned from percussionist Alla Rakha.
In 1989 he moved to New York City, where he has since worked. In 1991 he released his first album, which included the talent of Bob Mintzer, Kenny Werner, Peter Erskine, Marc Copland, and Marc Johnson. Since then he has played in the fusion genre, post-bop, hard bop, and jazz standards. Since the mid-1990s, Abbasi has operated as a music teacher, player, arranger and composer. In addition, he has worked as musical director and producer for singer Kiran Ahluwalia on her Juno award winning albums, Wanderlust (2008) and Aam Zameen (2011).
On his 2005 album Snake Charmer, which included Indian vocalist Kiran Ahluwalia, Abbasi combined jazz and Indian music in his compositions. He is currently working with three of his projects simultaneously: the Rez Abbasi Acoustic Quartet (RAAQ), which includes vibraphonist Bill Ware, bassist Stephan Crump, and drummer Eric McPherson; Rez Abbasi's Junction which includes Mark Shim on tenor sax/midi wind-controller, Ben Stivers on keyboards and Kenny Grohowski on drums. And with Vijay Iyer, Rudresh Mahanthappa, Johannes Weidenmüller, and Dan Weiss he formed a group called Invocation. They recorded the album Things to Come for Sunnyside Records (2009), which was chosen by Down Beat magazine as one of the best albums of the decade. Their second album is Suno Suno (2012) on the enja label. In addition, Abbasi was twice awarded the Chamber Music America New Jazz Works Grant in order to compose for Invocation.
- Third Ear' (Ozone, 1995)
- Modern Memory (EarthSounds 1996) with Tim Hagans, Gary Thomas Mike Formanek, Tony Moreno
- Out of Body (EarthSounds, 2002) with Tony Malaby, Ron Horton
- Snake Charmer (EarthSounds, 2003) with Dave Liebman, Gary Versace Kiran Ahluwalia, Dan Weiss
- Bazaar (Zoho, 2005)
- Things to Come (Sunnyside, 2009) Rudresh Mahanthappa, Vijay Iyer, Dan Weiss, Johannes Weidenmueller,Kiran Ahluwalia
- Natural Selection (Sunnyside, 2010) Bill Ware, Stephan Crump, Eric McPherson
- Suno Sono (Enja, 2012) Rudresh Mahanthappa, Vijay Iyer, Dan Weiss, Johannes Weidenmueller,Kiran Ahluwalia
- Continuous Beat (Enja, 2013) John Hebért, Satoshi Takeishi
- Intents & Purposes (Enja, 2015) Bill Ware, Stephan Crump, Eric McPherson
- Bielefeld Catalogue 1988 & 2002
- Richard Cook and Brian Morton: The Penguin Guide to Jazz Recordings, 8th Edition, London, Penguin, 2006 ISBN 0-141-02327 -9
- Rez Abbasi Management