This book (never translated into English) is of great historical significance. It is still worthy of study. Hausdorff was a leader in the second wave of set theory (post Cantor) and a founder of point-set topology. In his hands set theory became a tool for the working mathematician. This book still has the power to stir the mathematical heart. Even a jaded modern reader can learn much from it. There are many wonderful mathematical "set pieces"---a personal favorite is the continued fraction expansion of a pair of countable ordinals. The writing is concise, but not without touches of Hausdorff's literary polish.