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Starting with a review of geometric ideas in differential Calculus, the book leads the reader gently to a thorough study of the basic theory of differential manifolds and lie groups, and ends with an introduction to Riemannian Geometry. The book is written in a conversational tone and is ideal for self-study. All the concepts are well motivated and explained with concrete examples. The reader will find that lie groups are used as thematic examples, so that when ...
This book, taking a holistic view of geometry, introduces the reader to axiomatic, algebraic, analytic and differential geometry. Starting with an informal introduction to non-Euclidean plane geometries, the book develops the theory to put them on a rigorous footing. It may be considered as an explication of the Kleinian view of geometry ala Erlangen programme. The treatment in the book, however, goes beyond the Kleinian view of geometry. Some noteworthy topics ...