Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments, however, have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology). This book is a systematic exposition of the theory and a compilation of the main results in the field. The volume can be used for a one-semester undergraduate course in probability and differential geometry or as a complement to classical courses on differential geometry, Lie groups, or probability.