Greek ideas about geometry, straight-edge and compass constructions, and the nature of mathematical proof dominated mathematical thought for about 2,000 years. Projective geometry began its development in the Renaissance as artists like da Vinci and Durer explored methods for representing 3-dimensional objects on 2-dimensional surfaces. These ideas were refined and made increasingly abstract in the 19th and 20th centuries. Late in the 20th century, ideas from projective geometry found widespread application in the area of computer graphics. Similarly, Descartes's ideas about coordinate geometry led to progress in finding mathematical representations for shapes of increasing complexity, including the shape of the universe and other areas considered by mathematicians today. Covering the many aspects of geometry, this volume of the History of Mathematics series presents a compelling look at mathematical theories alongside historical occurrences. The engaging and informative text, complemented by photographs and illustrations, introduces students to the fascinating story of how geometry has developed. Biographical information on key figures, a look at different applications of geometry over time, and the groundbreaking discoveries related to geometry are comprehensively covered.