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Geometric Analysis combines differentiae equations and differential geometry．An important aspect is to solve geometric problems by studying differentiae equations．Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear．Particularly important example is the Monge-Amp~re equation。Applications to geometric problems have also motivated new methods and techniques in differential equations。The field of geometric analysis is broad and has had many striking applications．This handbook of geometric analysis provides introductions to and surveys of important topics in geometric analysis and their applications to related fields which is intend t0 be referred by graduate students and researchers in related areas．

Numerical Approximations to Extremal Metrics on Toric Surfaces .
R. S. Bunch, Simon K. Donaldson
1 Introduction
2 The set-up
3 Numerical algorithms: balanced metrics and refined approximations
4 Numerical results
5 Conclusions
References
Kahler Geometry on Toric Manifolds, and some other Manifolds with Large Symmetry
Simon K. Donaldson
Introduction
1 Background
2 Toric manifolds
3 Toric Fano manifolds
4 Variants of toric differential geometry
5 The Mukai-Umemura manifold and its deformations
References
Gluing Constructions of Special Lagrangian Cones
Mark Haskins, Nikolaos Kapouleas
I Introduction
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