Karlheinz Stockhausen (1928-2007) was one of the most influential composers of the second half of the twentieth century. Although his music has been written about extensively, there is little scholarship focusing directly on his saxophone music. This document is a study of Karlheinz Stockhausen's saxophone works. It introduces saxophonists, and others, to Stockhausen's idiomatic stylistic traits and techniques in the context of his saxophone pieces. Particular aspects of Stockhausen's creative output are illuminated, including the formal construction of his pieces, the visual component of his pieces, the spatialization of his pieces, and his use of electronic media. Six of Stockhausen's pieces are discussed in detail: In Freundschaft, Saxophon, Knabenduett, Linker Augentanz, Erwachen, and Edentia.