本书原版980页，是单卷本，为了便于读者阅读，影印版分为2卷。全面讲述最优输运——无论新老问题的专著。本书讲学严谨，基于大量的文献扩充改变而成，使得这本书成为一本相当有价值的宝典类书籍，证明完整自成体系，扩充了文献注解。适于最优输运方面的每个科研人员和研究生，博士及以上的人员不需要预备知识可以完全读懂该书。目次：导引；最优输运的量化描述；最优输运和黎曼几何；Ricci曲率的综合处理；结论和开放问题。

Preface
Conventions
Introduction
1Couplings and changes of variables
2Three examples of coupling techniques
3The founding fathers of optimal transport
Part ⅠQualitative description of optimal transport
4Basic properties
5Cyclical monotonicity and Kantorovich duality
6The Wasserstein distances
7Displacement interpolation
8The Monge-Mather shortening principle
9Solution of the Monge problem I: Global approach
10Solution of the Monge problem II: Local approach
11The Jacobian equationPreface
Conventions
Introduction
1Couplings and changes of variables
2Three examples of coupling techniques
3The founding fathers of optimal transport
Part ⅠQualitative description of optimal transport
4Basic properties
5Cyclical monotonicity and Kantorovich duality
6The Wasserstein distances
7Displacement interpolation
8The Monge-Mather shortening principle
9Solution of the Monge problem I: Global approach
10Solution of the Monge problem II: Local approach
11The Jacobian equation
12Smoothness
13Qualitative picture
Part ⅡOptimal transport and Riemannian geometry
14Ricci curvature
15Otto calculus
16Displacement convexity I
17Displacement convexity II
18Volume control
19Density control and local regularity
20Infinitesimal displacement convexity
21Isoperimetric-type inequalities
22Concentration inequalities
23Gradient flows I
24Gradient flows II: Qualitative properties
25Gradient flows III: Functional inequalities
Part ⅢSynthetic treatment of Ricci curvature
26Analytic and synthetic points of view
27Convergence of metric-measure spaces
28Stability of optimal transport
29Weak Ricci curvature bounds I: Definition and Stability
30Weak Ricci curvature bounds II: Geometric and analytic properties
Conclusions and open problems
References
List of short statements
List of figures
Index
Some notable cost functions

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