The saxophone isn't usually considered a classical music instrument. It's encountered far more often in jazz, blues and some modern pop music (the latter probably most famously - and allegedly almost by accident - in Gerry Rafferty's "Baker Street"). Nevertheless, some composers in the classical tradition have written for the saxophone.
Today I thought I'd turn to a US composer who's probably unknown to many of my readers (and was to me, until I moved to this country). I'll let Wikipedia introduce him.
Paul Creston (born Giuseppe Guttoveggio; October 10, 1906 – August 24, 1985) was an Italian American composer of classical music.
Born in New York City to Sicilian immigrants, Creston was self-taught as a composer. He was an honorary member of Phi Mu Alpha Sinfonia music fraternity, initiated into the national honorary Alpha Alpha chapter. His work tends to be fairly conservative in style, with a strong rhythmic element. His pieces include six symphonies, a number of concertos, including two for violin, one for marimba and orchestra (premiered by Ruth Stuber), one for one piano, one for two pianos, one for accordion and one for alto saxophone (the latter dedicated to Cecil Leeson), a fantasia for trombone and orchestra (composed for and premiered by Robert Marsteller), and a Rapsodie again for alto saxophone - written for Jean-Marie Londeix. He also wrote a suite (1935) and a sonata (op. 19, 1939) for alto saxophone and piano (both dedicated to Cecil Leeson), as well as a suite for organ, Op. 70. Several of his works were inspired by the poetry of Walt Whitman. He died in Poway, California, a suburb of San Diego.
Creston was one of the most performed American composers of the 1940s and 1950s. Several of his works have become staples of the wind band repertoire. Zanoni, Prelude and Dance and the Celebration Overture have been and still are on several state lists for contests across the USA.
Creston was also a notable teacher, with the composers Irwin Swack, John Corigliano, Elliott Schwartz, Frank Felice, and Charles Roland Berry, accordionist/composer William Schimmel and the jazz musicians Rusty Dedrick and Charlie Queener among his pupils. He wrote the theoretical books Principles of Rhythm (1964) and Rational Metric Notation (1979). He taught at Central Washington State College from 1968-1975.
There's more at the link.
Creston wrote a number of works for saxophone. Here are two of them. Let's start with his Sonata for alto saxophone and piano, Op. 19, composed in 1939.
Next, for a more orchestral experience (heavily flavored by blues and jazz rhythms), here's his Concerto for alto saxophone, Op. 26, written in 1944.
An interesting variation on orchestral themes, with some foot-tapping sections that probably infuriated the "old school" of classical musicians at the time it was first performed.