图所著的《流形导论（第2版）（英文版）》将代数、拓扑和分析几个领域结合起来，流形已经很好地应用在经典力学、广义相对论和量子场论等多个领域。

本书直达主题，流形的讲述旨在帮助读者更快地了解这个科目的本质，书中提供了许多练习和问题的提示和解答，可供读者参考。

Preface to the Second Edition

Preface to the First Edition

A Brief Introduction

Chapter 1 Euclidean Spaces

 1 Smooth Functions on a Euclidean Space

1.1 C∞ Versus Analytic Functions

1.2 Taylor's Theorem with Remainder

Problems

 2 Tangent Vectors in Rn as Derivations

2.1 The Directional Derivative

2.2 Germs of Functions

2.3 Derivations at a Point

2.4 Vector Fields

2.5 Vector Fields as Derivations

Problems

 3 The Exterior Algebra of Multicovectors

3.1 Dual Space

3.2 Permutations

3.3 Multilinear Functions

3.4 The Permutation Action on Multilinear Functions

3.5 The Symmetrizing and Alternating Operators

3.6 The Tensor Product

3.7 The Wedge Product

3.8 Anticommutativity of the Wedge Product

3.9 Associativity of the Wedge Product

3.10 A Basis for k—Covectors

……

Chapter 2 Manifolds

Chapter 3 The Tangent Space

Chapter 4 Lie Groups and Lie Algebras

Chapter 5 Differential Forms

Chapter 6 Integration

Chapter 7 De Rham Theory