Answer by taking a quote from the following article:

Keith Jarrett (born May 8, 1945) is an American jazz and classical music pianist. Jarrett started his career with Art Blakey, moving on to play with Charles Lloyd and Miles Davis. Since the early 1970s he has enjoyed a great deal of success as a group leader and a solo performer in jazz, jazz fusion, and classical music. His improvisations draw from the traditions of jazz and other genres, especially Western classical music, gospel, blues, and ethnic folk music.

From 1971 to 1976, Jarrett added saxophonist Dewey Redman to the existing trio with Haden and Motian (who produced one more album as a trio, called The Mourning of A Star for Atlantic Records in 1971). The so-called "American quartet" was often supplemented by an extra percussionist, such as Danny Johnson, Guilherme Franco, or Airto Moreira, and occasionally by guitarist Sam Brown. The quartet members played various instruments, with Jarrett often being heard on soprano saxophone and percussion as well as piano; Redman on musette, a Chinese double-reed instrument; and Motian and Haden on a variety of percussion. Haden also produced a variety of unusual plucked and percussive sounds with his acoustic bass, even running it through a wah-wah pedal for one track ("Mortgage on My Soul", on the album Birth). The group recorded two albums for Atlantic Records in 1971, El Juicio (The Judgement) and Birth; another on Columbia Records called Expectations (that included guitar by Sam Brown, plus string and brass arrangements and for which Jarrett's contract with the label was terminated within a month of its release); eight albums on Impulse! Records; and two on ECM.  Byablue and Bop-Be, albums recorded for Impulse!, mainly feature the compositions of Haden, Motian and Redman, as opposed to Jarrett's own, which dominated the previous albums. Jarrett's compositions and the strong musical identities of the group members gave this ensemble a very distinctive sound. The quartet's music is an amalgam of free jazz, straight-ahead post-bop, gospel music, and exotic, Middle-Eastern-sounding improvisations.  In the mid/late 1970s, concurrently with the American quartet, Jarrett led a "European quartet" which was recorded by ECM. This combo consisted of saxophonist Jan Garbarek, bassist Palle Danielsson, and drummer Jon Christensen. They played in a style similar to that of the American quartet, but with many of the avant-garde and Americana elements replaced by the European folk and classical music influences that characterized the work of ECM artists at the time.  Jarrett became involved in a legal wrangle following the release of the album Gaucho in 1980 by the U.S. rock band Steely Dan. The album's title track, credited to Donald Fagen and Walter Becker, bore a resemblance to Jarrett's "Long As You Know You're Living Yours", from Jarrett's European quartet 1974 Belonging album. When a Musician magazine interviewer pointed out the similarity, Becker admitted that he loved the Jarrett composition and Fagen said they had been influenced by it. After their comments were published, Jarrett sued, and Becker and Fagen were forced to add his name to the credits and to include him in the royalties.

Who are the quartets?
From 1971 to 1976, Jarrett added saxophonist Dewey Redman to the existing trio with Haden and Motian