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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 he finishes the theory of differential manifolds, he has learnt all basic results of the theory of lie groups except Cartan’s theorem. The proof of Frobenius theorem, the geometric interpretation of the lie bracket, the constant reconciliation of the modern view point with the classical approach, especially in tensor analysis, and the illustration of all concepts in lie groups in the context of linear lie groups are noteworthy features of this book.