由马多雷编著的《非交换微分几何及其在物理学中的应用导论》是以1994年作者在LMS的讲演稿为蓝本。这是第2版，在第1版的基础上做了大量的修订，增加了不少有关实条件和线性联络的新材料和Jordan变形和量子Euclidean空间，具有基本的常微分几何知识和纤维丛理论就可以完全理解这些知识。

1 Introduction

2 Differential Geometry

 2.1 Diiferential manifolds

 2.2 Metrics and connections

 2.3 Cohomology

3 Matrix Geometry

 3.1 Differential forms Ⅰ

 3.2 Differential forms Ⅱ

 3.3 Tensor products

 3.4 Metrics

 3.5 Yang-Mills connections

 3.6 Linear connections

 3.7 Curvature

4 Noncommutative Geometry

 4.1 General algebras

 4.2 Poisson structures

 4.3 Topological algebras

 4.4 Quantum groups

5 Vector Bundles

 5.1 K-theory

 5.2 A matrix analogue

 5.3 Predholm modules

6 Cyclic Homology

 6.1 The universal calculus

 6.2 Cyclic homology

 6.3 Morita equivalence

 6.4 The Loday-QuiUen theorem

7 Modifications of Space-Time

 7.1 Noncommutative space-time

 7.2 A finite model

 7.3 Fuzzy physics

8 Extensions of Space-Time

 8.1 The spinning particle

 8.2 Noncommutative electrodynamics

 8.3 Modified Kaluza-Klein theory