He was born to a Jewish family in Mannheim, Germany and fled to the United States in 1939. Educated at Boston University, he taught at the Eastman School of Music in Rochester, New York from 1966 until his retirement in 1994. He is the author of three books, Choral Conducting (Holt Reinhart and Winston 1971, second edition Schirmer Books 1985), Sight Singing (W.W. Norton 1979, 1997), and The Study of Orchestration (W.W. Norton 1982, 1989, 2001). He has also contributed numerous articles to major magazines and books published in the U.S. and abroad.

He has been awarded many prizes including a just awarded membership into the American Academy and Institute of Arts and Letters, the Charles Ives Award, the Lillian Fairchild Award, etc. In 1983, he won the Deems Taylor Award for his book on orchestration; in 1984, he was appointed Honorary Professorial Fellow of the University College in Cardiff, Wales, and was awarded a Guggenheim Fellowship for 1984-85. He has been a MacDowell Fellow for five years between 1954 and 1963. In 1986 he received the "Distinguished Alumni Award" from Boston University. The Music Teachers' National Association selected Adler as its "Composer of the Year 1986-87" for Quintalogues, which won the national competition. In the 1988-89 year, he has been designated "Phi Beta Kappa Visiting Scholar." In 1989, he was awarded The Eastman School's Eisenhart Award for distinguished teaching, and he has been given the honor of Composer of the Year (1991) for the American Guild of Organists. During his second visit to Chile, Adler was elected to the Chilean Academy of Fine Arts (1993) "for his outstanding contributions to the world of music as composer, conductor, and author."

Adler's catalog includes over 400 published works in all media including five operas, six symphonies, eight string quartets, eight concerti (organ, piano, violin, cello, flute, guitar, saxophone quartet, woodwind quintet), many shorter orchestral works, works for wind ensemble and band, chamber music, a great deal of choral music and songs.