An Expedition to Geometry

This book is written as an attempt to entice the students of math- ematics to the world of geometry. In spite of the great strides made in modern geometry at research level, there is no introductory book which gives modern aspects of geometry at undergraduate/graduate level. Our book is an attempt to fill this vacuum. In this endeavor, we have taken great care in the selection of topics and their treatment. Our guiding principles are 1. to cultivate geometrie intuition in readers, 2. to give a panoramic view of various facets of geometry, 3. to give a modern treatment of intuitively appealing classical re- sults, and 4. to employ as much as possible the methods which are close to the ones adopted in contemporary geometry. Some of the material in this book has already been used in the Math- ematics Training and Talent Search (MTTS) Programme and at various other places. The response to the course has been very enthusiastic both from students and teachers. Many of them insisted on our bring- ing out the privately circulated notes in book form. This book is thus an outcome of the cumulative effects of such requests. Unlike some books on geometry, our work takes a holistic view of geometry. It introduces the readers to axiomatic, algebraic, analytic and differential geometry.