One of the most important (if low-key) guitarists in jazz history, Jim Hall has been releasing albums since the '50s. Live at Birdland captures The Jim Hall Quartet performing at the well-known New York City club in 2010. Hall, alto saxophonist Greg Osby, drummer Joey Baron, and bassist Steve Laspina make up the band. The Hall original “Furnished Flats,” with its springy theme, opens the set. Hall immediately gets down to business with a solo full of slashing chords that continually excite. Osby follows with an inventive statement, and Laspina and Baron also get their say. Then a version of Jerome Kern’s “All the Things You Are” starts with a lovely unaccompanied guitar intro. The band joins in, quietly swinging behind Hall and Osby, who nicely explore the standard. “Friendly Recollections” is an impressionistic duet for guitar and drums, the sort of track where a fluttering brushstroke or sustained electric tone speaks volumes. On the Sonny Rollins–penned “St. Thomas,” Hall really cuts loose. And Osby navigates the rhythms of the Caribbean-flavored piece with great aplomb, wrapping up the album in a lively fashion.