![]() ![]() ![]() ), borrows many ideas from Riemannian or metric geometry. In another direction, Geometric Group Theory, a very active field nowadays (cf. These have been followed, quite recently, by a possibly successful approach to the Poincaré conjecture. In this respect, we can quote the major breakthroughs in four-dimensional topology which occurred in the eighties and the nineties of the last century (see for instance ). It has proved to be a precious tool in other parts of mathematics. However, Riemannian Geometry is not only a fascinating field in itself. The reader can consult for instance the recent book. During these years, Riemannian Geometry has undergone many dramatic developments. However, the encouragements of various readers and friends have persuaded us to write this third edition. Many years have passed since the first edition. ![]()
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