Inversions are transformations of geometric figures, under which straight lines may be mapped to circles, and conversely. The use of such mapping allows development of a unified method of solution for many of the problems of elementary geometry, especially those concerning constructions and "pencils" of curves. This book discusses the inversion transformations and their applications. In the first chapter, inversion transformations and their applications to questions in elementary geometry are studied. In the second chapter, transformations are expressed as linear and linear-fractional functions of a complex variable. In the third chapter, the foundations of geometry are presented from the standpoint of group theory. (Author/MK)