Lawrence Conlon auth. The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the first or second year graduate student preparing for advanced courses and seminars in differential topology and geometry. Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists wishing to survey the field.

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Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text.

Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists wishing to survey the field. The themes of linearization, re integration, and global versus local calculus are emphasized throughout.

Additional features include a treatment of the elements of multivariable calculus, formulated to adapt readily to the global context, an exploration of bundle theory, and a further optional development of Lie theory than is customary in textbooks at this level.

Students, teachers and professionals in mathematics and mathematical physics should find this a most stimulating and useful text. The subject matter is differential topology and geometry, that is, the study of curves, surfaces and manifolds where the assumption of differentiability adds the tools of differentiable and integral calculus to those of topology. Within this area, the book is unusually comprehensive The style is clear and precise, and this makes the book a good reference text.

There are many good exercises. The presentation is smooth, the choice of topics optimal, and the book can be profitably used for self teaching.

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## Differentiable Manifolds

The presentation is smooth, the choice of topics optimal, and the book can be profitably used for self teaching. Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists wishing to survey the field. The themes of linearization, re integration, and global versus local calculus are emphasized throughout. Additional features include a treatment of the elements of multivariable calculus, formulated to adapt readily to the global context, an exploration of bundle theory, and a further optional development of Lie theory than is customary in textbooks at this level. New to this edition is a detailed treatment of covering spaces and the fundamental group.

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Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which, in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists wishing to survey the field. The themes of linearization, re integration, and global versus local calculus are emphasized throughout. Additional features include a treatment of the elements of multivariable calculus, formulated to adapt readily to the global context, an exploration of bundle theory, and a further optional development of Lie theory than is customary in textbooks at this level. Students, teachers and professionals in mathematics and mathematical physics should find this a most stimulating and useful text.

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