●Preface
Chapter 1. Metric Spaces
1.1. Definitions
1.2. Examples
1.3. Metrics and Topology
1.4. Lipschitz Maps
1.5. Complete Spaces
1.6. Compact Spaces
1.7. Hausdorff Measure and Dimension

Chapter 2. Length Spaces
2.1. Length Structures
2.2. First Examples of Length Structures
2.3. Length Structures Induced by Metrics
2.4. Characterization of Intrinsic Metrics
2.5. Shortest Paths
2.6. Length and Hausdorff Measure
2.7. Length and Lipschitz Speed

Chapter 3. Constructions
3.1. Locality， Gluing and Maximal Metrics
3.2. Polyhedral Spaces
3.3. Isometries and Quotients
3.4. Local Isometries and Coverings
3.5. Arcwise Isometries
3.6. Products and Cones

Chapter 4. Spaces of Bounded Curvature
4.1. Definitions
4.2. Examples
4.3. Angles in Alexandrov Spaces and Equivalence of Definitions
4.4. Analysis of Distance Functions
4.5. The First Variation Formula
4.6. Nonzero Curvature Bounds and Globalization
4.7. Curvature of Cones

Chapter 5. Smooth Length Structures
5.1. Riemannian Length Structures
5.2. Exponential Map
5.3. Hyperbolic Plane
5.4. Sub-Riemannian Metric Structures
5.5. Riemannian and Finsler Volumes
5.6. Besikovitch Inequality

Chapter 6. Curvature of Riemannian Metrics
6.1. Motivation： Coordinate Computations
6.2. Covariant Derivative
6.3. Geodesic and Gaussian Curvatures
6.4. Geometric Meaning of Gaussian Curvature
6.5. Comparison Theorems

Chapter 7. Space of Metric Spaces
7.1. Examples
7.2. Lipschitz Distance
7.3. Gromov-Hausdorff Distance
7.4. Gromov-Hausdorff Convergence
7.5. Convergence of Length Spaces

Chapter 8. Large-scale Geometry
8.1. Noncompact Gromov-Hausdorff Limits
8.2. Tangent and Asymptotic Cones
8.3. Quasi-isometries
8.4. Gromov Hyperbolic Spaces
8.5. Periodic Metrics

Chapter 9. Spaces of Curvature Bounded Above
9.1. Definitions and Local Properties
9.2. Hadamard Spaces
9.3. Fundamental Group of a Nonpositively Curved Space
9.4. Example： Semi-dispersing Billiards

Chapter 10. Spaces of Curvature Bounded Below
10.1. One More Definition
10.2. Constructions and Examples
10.3. Toponogov's Theorem
10.4. Curvature and Diameter
10.5. Splitting Theorem
10.6. Dimension and Volume
10.7. Gromov-Hausdorff Limits
10.8. Local Properties
10.9. Spaces of Directions and Tangent Cones
10.10. Further Information
Bibliography
Index

“度量幾何”是建立在拓撲空間長度概念基礎之上的處理幾何的方法，這種方法在最近幾十年飛速發展，並滲透到諸如群論、動力繫統和偏微分方程等其他數學學科。
《度量幾何學教程（英文版）》有兩個目標：詳細闡述長度空間理論中使用的基本概念和技巧，以及為大量不同的幾何論題提供一個初等導引，這些論題都與距離觀念相關，包括黎曼度量和Carnot-Caratheodory度量、雙曲平面、距離-體積不等式、（大規模的、粗糙的）漸近幾何、Gromov雙曲空間、度量空間的收斂性以及Alexandrov空間（非正和非負的彎曲空間）。作者傾向於用“易於看見”的方法來處理“易於觸踫”的數學對像。
作者設定了一個具有挑戰性的目標，即讓《度量幾何學教程（英文版）》的核心部分能為一年級研究生所接受。大多數新的概念和方法都按最簡單的情形來提出並闡明，從而避免了技術性的障礙。書中還包括大量習題，這些習題是《度等