This book examines interactions of polyhedral discrete geometry and algebra. What makes this book different from others is the presentation of several central results in all three areas of the exposition - discrete geometry commutative algebra and K-theory. The only prerequisite for the reader is a background in algebra and the basics of polyhedral geometry have been included in Chapter 1. The text will be of interest to graduate students and mathematicians. Included are numerous exercises historical background and notes throughout the chapters.