The present volume is Part I of Geometric Transformations by I. M. Yaglom. The Russian original appeared in three parts; Parts I and II were published in 1955 in one volume of 280 pages. Part III was published in 1956 as a separate volume of 611 pages. In the English translation Parts I and II are published as two separate volumes: NML 8 and NML21. The first chapter of Part III, on projective and some non-Euclidean geometry, was translated into English and published in 1973 as NML vol. 24; the balance of Part III, on inversions, has not so far been published in English.

In this translation most references to Part III were eliminated, and Yaglom's “Foreword” and “On the Use of This Book” appear, in greatly abbreviated form, under the heading “From the Author's Preface”.

This book is not a text in plane geometry. On the contrary, the author assumes that the reader is already familiar with the subject. Most of the material could be read by a bright high school student who has had a term of plane geometry. However, he would have to work; this book, like all good mathematics books, makes considerable demands on the reader.

The book deals with the fundamental transformations of plane geometry, that is, with distance-preserving transformations (translations, rotations, reflections) and thus introduces the reader simply and directly to some important group theoretic concepts.