Old and New Topics in Geometry

A decade long experience of teaching the course "Fundamental of Geometry", many notes for exercises, and endless extra reading are the bases for this bulky work. The online manuscript already includes many topics with many exercises including solutions and hundreds a elaborate computer generated drawings.The first volume begins with Hilbert's axioms from the Foundations of Geometry,and goes on to projective, neutral and basic Euclidean geometry.The present second volume deals with many more advanced topics form Euclidean geometry andcontains a long treatise about hyperbolic geometry.Here the disk models of Poincar\'e and Klein are used to do a lot of constructions, using straightedge and compass from the background Euclidean geometry.Too, Hilbert's axiomatic approach based on the asymptotic rays, is explained from the beginning up to the reconstruction of the Poincar\'e disk model. The last section gives a short course on Gauss' differential geometry and the pseudo sphere.