本书内容是几何分析领域很好的科研工作者所写的综述性报告，文章汇报了几何分析领域的前沿热点。包括包括：偏微分方程和黎曼几何、不变体系、几何可变体系、瞬变体系和刚片、自由度与辛几何、代数几何和物理中的超弦理论、二维非线性偏微分方程、Ricci流、Gromov-Witten不变量理论、Kaehler-Ricci流，Kaehler-Ricci孤立子专享性，调和映射紧性，高余维平均曲率流等。
本书适合高年级本科生，研究生和相关领域的科研工作者阅读参考。

Prologue
Recent Progress on the Formation of Trapped Surfaces and Black Holes
Notes on Weighted K.hler-Ricci Solitons
A Monge-Ampère Type Functional and Related Prescribing Curvature Problems
The Obata Type Integral Identity and Its Application
A Brief Survey on a Recent Generalization of Cohn-Vossen Inequality on Certain K.hler Manifolds
A Brief Summary of the Recent Global Regularity for Monge-Ampère Equations
Isoparametric Submanifolds and Mean Curvature Flow
Isolated Singularities of the Yamabe Equation with Non-flat Metrics
The Optimal Exponent of Certain Moser-Trudinger Type Inequalities on Projective Manifolds
Lower Bound of Modified K-energy on a Fano Manifold with Degeneration for K.hler-Ricci Solitons
Some Regularity Estimates of the Complex Monge-Ampère Equation
Topology of Surfaces with Finite Willmore Energy
Finite Generation and the K.hler-Ricci Soliton Degeneration