Published by . Isaac Moiseevich Yaglom's two-volume book "Geometric Transformations" is undoubtedly one of the main, reference books for schoolchildren who study geometry deeply, serves as a valuable help for their teachers for many decades. The book was published in the 50s in a relatively small print run (1st volume - 1955, 25,000, 2nd volume - 1956, 15,000). Paper versions of this remarkable book have long become a bibliographic rarity and are not available in all even large libraries. by the author. The present second volume of Geometric Transformations is devoted to the so-called linear and circular transformations. which are held at the mathematical departments of pedestals and universities , but are not affected at all by the secondary school program (in universities these transformations are more often called projective and conformal). However, this book is addressed primarily to readers, one way or another connected with high school, students and teachers of schools, students and teachers of institutes .. Accordingly, its main purpose is to show the close relationship of the transformations considered here with elementary geometry. The author had to abandon the presentation of higher theories related to geometric transformations almost completely, since the book already turned out to be thicker than he would like. The only significant deviations to the field of "higher geometry" are the annexes to Chapters I and II devoted to Lobachevsky's non-Euclidean geometry. However, here the author aspired to the maximum elementary, so that these applications should also be quite accessible to high school students interested in mathematics. A significant part of the content of the book is the tasks, accompanied by the solutions given at the end of .. Content. Foreword by . Part Three . LINEAR AND ROUND TRANSFORMATIONS . Introduction. What is geometry? (End). Chapter I. Linear transformations. ? 1. Parallel plane-to-plane design. Linear plane transformations. ? 2. Central plane-to-plane design. Generalized linear (projective) plane transformations. ? 3. Central design that converts a given circle to a circle. Stereographic projection. ? 4. Polar plane transformation. The Principle of Duality . ? 5. Projective transformations of line and circle. Building with a single line. Annex to Chapter . I. Lobachevsky's non-Euclidean geometry (first exposition). Chapter II. Circular transformations. ? 1. Symmetry with respect to circumference (inversion). ? 2. Application of inversion to construction tasks. Building with a single circuit. ? 3. Bundles of circles. Radical axis of two circles . ? 4. Inversion (end). ? 5. Axial circular transformation. Annex to Chapter . II. Non-Euclidean geometry of Lobachevsky (second exposition). TASK SOLUTIONS. Chapter I. Linear transformations. Chapter II. Circular transformations. List of problems, other solutions of which are contained in other books. Subject Index. Other issues of the series on the website. Issue. 1 - Chentsov N. N. , Shklyarsky D. About. , Yaglom I. M. Selected Problems and Theorems of Elementary Mathematics . Arithmetic and Algebraic . Issue. 2 - Chentsov N. N. , Shklyarsky D. About. , Yaglom I. M. Selected Problems and Theorems of Elementary Mathematics . Geometry (planimetry), Vyp. 3 - Chentsov N. N. , Shklyarsky D. About. , Yaglom I. M. Selected Problems and Theorems of Elementary Mathematics . Geometry (stereometry), Vyp. 4 - Boltyansky V. G. , Yaglom I. M. Convex Figures . Issue. 5 - Yaglom I. M. , Yaglom A. M. Non-elementary tasks in elementary presentation. Issue. 6 - Dynkin E. B. , Uspensky V. A. Mathematical Conversations . Issue. 7 - Yaglom I. M. Geometric transformations. Volume 1. Buy the book: urss. ru