Old and New Topics in Geometry

<p>A decade long experience of teaching the course Fundamental of Geometry </p><p>many notes for exercises and endless extra reading are the bases for this bulky work.</p><p>    The online manuscript already includes many topics with many exercises including solutions and hundreds a elaborate computer generated drawings.</p><p><br></p><p>The first volume begins with Hilbert's axioms from the Foundations of Geometry</p><p>and goes on to projective neutral and basic Euclidean geometry.</p><p>The present second volume deals with many more advanced topics form Euclidean geometry and</p><p>contains a long treatise about hyperbolic geometry.</p><p>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.</p><p>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.</p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p><p><br></p>