This book contains selected topics from the history of geometry, with "modern" proofs of some of the results, as well as a fully modern treatment of selected basic issues in geometry. It is geared towards the needs of future mathematics teachers. All too often the geometry which goes into the syllabus for these students presents the material in a pedantic and formalistic style, suppressing its dynamic character and its role as part of the foundation of our common cultural heritage. As such, one of my goals is to open up these aspects of the field; another is to extend an invitation to mathematics in general. It is an unfortunate fact that today, at a time when mathematics and knowledge of mathematics are more important than ever, phrases like math avoidance and math anxiety are very much in the public vocabulary. Making a serious effort to heal these ills is an essential task. Thus the book also aims at an informed public, interested in making a new beginning in math.For the 2nd edition, some of the historical material giving historical context has been expanded and numerous illustrations have been added. The main difference is however the inclusion of a large number of exercises with some suggestions for solutions.For excerpts from reviews from the first edition have a look at http://www.springer.com/978-3-540-41949-5.