On one hand, geometry refers to two- and three-dimensional Euclidean geometry, the elementary geometry that is also taught in schools, dealing with points, lines, planes, distances, angles, etc., as well as the conceptual formations and methods developed through a systematic and mathematical treatment of this subject. On the other hand, the term geometry encompasses a number of major subfields of mathematics. The author describes in this textbook the five groups of axioms, the theory of proportions and areas in the plane, the Desargues' and Pascal's theorems, and much more. Illustrated with numerous figures. Reprint of the original edition from 1903.