riable calculus, the leap from Euclidean space to manifolds can often be difficult. It takes time and patience, and it is easy to become mirred in abstraction and generalization.

In this text the author draws on his extensive experience in teaching this subject to minimize these difficulties. The pace is relatively liesurely, inessential abstraction and generality are avoided, the essential ideas used from the prerequisite subjects are reviewed, and there is an abundance of accessible and carefully developed examples to illuminate new concepts and to motivate the reader by illustrating their power. There are more than 400 exercises for the reader.

This book has been in constant, successful use for more than 25 years and has helped several generations of students as well as working mathemeticians, physicists and engineers to gain a good working knowledge of manifolds and to appreciate their importance, beauty and extensive applications.

This textbook covers the essential concepts of differentiable manifold and Riemannian geometry, using detailed examples to walk the reader through the transition from Euclidean space to manifolds. Excessive abstraction and generalities are avoided. Chapters concentrate on manifolds, functions and mappings, submanifolds, vector fields, tensors, integration, differentiation, and curvature. Boothby teaches at Washington University in St. Louis.
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In this text the author draws on his extensive experience in teaching this subject to minimize these difficulties. The pace is relatively liesurely, inessential abstraction and generality are avoided, the essential ideas used from the prerequisite subjects are reviewed, and there is an abundance of accessible and carefully developed examples to illuminate new concepts and to motivate the reader by illustrating their power. There are more than 400 exercises for the reader.

This book has been in constant, successful use for more than 25 years and has helped several generations of students as well as working mathemeticians, physicists and engineers to gain a good working knowledge of manifolds and to appreciate their importance, beauty and extensive applications.

has helped several generations of students as well as working mathemeticians, physicists and engineers to gain a good working knowledge of manifolds and to appreciate their importance, beauty and extensive applications.

William Boothby received his Ph.D. at the University of Michigan and was a professor of mathematics for over 40 years. In addition to teaching at Washington University, he taught courses in subjects related to this text at the University of Cordoba (Argentina), the University of Strasbourg (France), and the University of Perugia (Italy).William Boothby received his Ph.D. at the University of Michigan and was a professor of mathematics for over 40 years. In addition to teaching at Washington University, he taught courses in subjects related to this text at the University of Cordoba (Argentina), the University of Strasbourg (France), and the University of Perugia (Italy).

ds on a Manifold; Tensors and Tensor Fields on Manifolds; Integration on Manifolds; Differentiation on Riemannian Manifolds; Curvature; Index