前辅文
 Chapter 1. K¨ahler Geometry
  1.1. Complex manifolds
  1.2. Almost complex structures
  1.3. Hermitian and K¨ahler metrics
  1.4. Covariant derivatives and curvature
  1.5. Vector bundles
  1.6. Connections and curvature of line bundles
  1.7. Line bundles and projective embeddings
 Chapter 2. Analytic Preliminaries
  2.1. Harmonic functions on Rn
  2.2. Elliptic differential operators
  2.3. Schauder estimates
  2.4. The Laplace operator on K¨ahler manifolds
 Chapter 3. K¨ahler-Einstein Metrics
  3.1. The strategy
  3.2. The C0- and C2-estimates
  3.3. The C3- and higher-order estimates
  3.4. The case c1(M) = 0
  3.5. The case c1(M) >0
  3.6. Futher reading
 Chapter 4. Extremal Metrics
  4.1. The Calabi functional
  4.2. Holomorphic vector fields and the Futaki invariant
  4.3. The Mabuchi functional and geodesics
  4.4. Extremal metrics on a ruled surface
  4.5. Toric manifolds
 Chapter 5. Moment Maps and Geometric Invariant Theory
  5.1. Moment maps
  5.2. Geometric invariant theory (GIT)
  5.3. The Hilbert-Mumford criterion
  5.4. The Kempf-Ness theorem
  5.5. Relative stability
 Chapter 6. K-stability
  6.1. The scalar curvature as a moment map
  6.2. The Hilbert polynomial and flat limits
  6.3. Test-configurations and K-stability
  6.4. Automorphisms and relative K-stability
  6.5. Relative K-stability of a ruled surface
  6.6. Filtrations
  6.7. Toric varieties
 Chapter 7. The Bergman Kernel
  7.1. The Bergman kernel
  7.2. Proof of the asymptotic expansion
  7.3. The equivariant Bergman kernel
  7.4. The algebraic and geometric Futaki invariants
  7.5. Lower bounds on the Calabi functional
  7.6. The partial C0-estimate
 Chapter 8. CscK Metrics on Blow-ups
  8.1. The basic strategy
  8.2. Analysis in weighted spaces
  8.3. Solving the non-linear equation when n > 2
  8.4. The case when n = 2
  8.5. The case when M admits holomorphic vector fields
  8.6. K-stability of cscK manifolds
 Bibliography
 Index