This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants. Also included are complete proofs, introduction of coordinates, the theory of area, geometrical constructions and finite field extensions, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra. The text is intended for junior-senior level mathematics majors. This book offers a unique opportunitiy to understand the essence of one of the great thinkers of western civilization. A guided reading of Eulid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs, introduction of coordinates, the theory of area, geometrical condtructions and finite field extensions, history of the parallel postulate, the various non-Eclidean geometries, and the regular and semi-regular polyhedra. The text is intended for junior-senior level college mathematics majors.