Piotr T. Chrusciel & Helmut Friedrich 
Einstein Equations and the Large Scale Behavior of Gravitational Fields [PDF ebook] 
50 Years of the Cauchy Problem in General Relativity

The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out.Background material on techniques in PDE theory, differential geometry, and causal theory is provided.