This book is an outgrowth of a graduate level course taught for several years at Rensselaer Polytechnic Institute (RPI). When the course started in the early 1990s, there were only two textbooks available that taught signal compression, Jayant and Noll and Gersho and Gray. Certainly these are excellent textbooks and valuable references, but they did not teach some material considered to be necessary at that time, so the textbooks were supplemented with handwritten notes where needed. Eventually, these notes grew to many pages, as the reliance on published textbooks diminished. The lecture notes remained the primary source even after the publication of the excellent book by Sayood, which served as a supplement and a source of some problems. While the Sayood book was up to date, well written, and authoritative, it was written to be accessible to undergraduate students, so lacked the depth suitable for graduate students wanting to do research or practice in the field. The book at hand teaches the fundamental ideas of signal compression at a level that both graduate students and advanced undergraduate students can approach with confidence and understanding. The book is also intended to be a useful resource to the practicing engineer or computer scientist in the field. For that purpose and also to aid understanding, the 40 algorithms listed under Algorithms in the Index are not only fully explained in the text, but also are set out step-by-step in special algorithm format environments.