Part I Euclidean Geometry of the plane -- 1 The basic notions -- 2 Circle and polygons -- 3 Areas, Thales, Pythagoras, Pappus -- 4 The power of the circle -- 5 From the classical theorems.

This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics. The book is based on lecture notes from more than 30 courses which have been taught over the last 25 years. Using a synthetic approach, it discusses topics in Euclidean geometry ranging from the elementary (axioms and their first consequences), to the complex (the famous theorems of Pappus, Ptolemy, Euler, Steiner, Fermat, Morley, etc.). Through its coverage of a wealth of general and specialized subjects, it provides a comprehensive account of the theory, with chapters devoted to basic properties of simple planar and spatial shapes, transformations of the plane and space, and conic sections. As a result of repeated exposure of the material to students, it answers many frequently asked questions. Particularattention has been given to the didactic method; the text is accompanied by a plethora of figures (more than 2000) and exercises (more than 1400), most of them with solutions or expanded hints. Each chapter also includes numerous references to alternative approaches and specialized literature. The book is mainly addressed to students in mathematics, physics, engineering, school teachers in these areas, as well as, amateurs and lovers of geometry. Offering a sound and self-sufficient basis for the study of any possible problem in Euclidean geometry, the book can be used to support lectures to the most advanced level, or for self-study.