作者介绍了经典极小曲面理论最近取得的巨大成果。三维欧氏空间中极小平面域的分类是本书的重点。分类的证明有赖许多当前活跃的顶尖数学家的工作，从而触及该领域中许多最重要的结果。通过极小平面域分类的故事，读者可以领略这一理论的内在美，了解作者对这一非常经典的学科当前进展的看法。
本书包括该理论的最新研究进展，如Colding-Minicozzi理论、极小层压、开口空间的排序定理、极小曲面的共形结构、具有无限全曲率的极小环形开口、嵌入Calabi-Yau问题、曲率和拓扑尺度上的局部图像、局部可去奇点定理、有限亏格的嵌入极小曲面、极小曲面的拓扑分类、Scherk单周期极小曲面的唯一性，以及未解决的问题和猜想等。

Preface
1. Introduction
2. Basic results in classical minimal surface theory
2.1 Eight equivalent definitions of minimality
2.2 Weierstrass representation
2.3 Minimal surfaces of finite total curvature
2.4 Periodic minimal surfaces
2.5 Some interesting examples of complete minimal surfaces
2.6 Monotonicity formula and classical maximum principles
2.7 Ends of properly embedded minimal surfaces
2.8 Second variation of area, index of stability and Jacobi functions
2.9 Barrier constructions
3. Minimal surfaces with finite topology and more than one end
3.1 Classification results for embedded minimal surfaces of finite total curvature
3.2 Constructing embedded minimal surfaces of finite total curvature
4. Limits of embedded minimal surfaces without local area or curvature bounds
4.1 Colding-Minicozzi theory
4.1.1 Main strategy of the proof of Theorem 4.1.3.
4.1.2 More details on the main strategy
4.2 Minimal laminations with isolated singularities
5. The structure of minimal laminations of R3
6. The Ordering Theorem for the space of ends
7. Conformal structure of minimal surfaces
7.1 Recurrence and parabolicity for manifolds
7.2 Universal superharmonic functions
7.3 Quadratic area growth and middle ends
8. Uniqueness of the helicoid I: Proper case
9. Embedded minimal annular ends with infinite total curvature
9.1 Harmonic functions on annuli
9.2 Annular minimal ends of infinite total curvature
10. The embedded Calabi-Yau problem
10.1 Uniqueness of the helicoid II: Complete case
10.2 Regularity of the singular set of convergence of a limit minimal lamination
11. Local pictures, local removable singularities and dynamics
12. Embedded minimal surfaces of finite genus
12.1 The Hoffman-Meeks conjecture
12.2 Non-existence of one-limit-ended examples
12.3 Uniqueness of the Riemann minimal examples
12.4 Colding-Minicozzi theory (fixed genus)
13. Topological aspects of minimal surfaces
14. Partial results on the Liouville Conjecture
15. The Scherk Uniqueness Theorem
16. Calabi-Yau problems
17. Outstanding problems and conjectures
Bibliography