This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.

中文翻译：

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爱因斯坦方程的存在性和全局动力学定理。

本文是爱因斯坦方程解的存在性和全局动力学定理指南。它提请人们注意该领域的开放性问题。对相对较好理解的时域柯西问题进行了研究。讨论了具有各种类型对称性的解的全局结果。提供了牛顿理论和狭义相对论的精选结果，提供了有用的比较。给出了小数据情况下全局结果的处理以及用规定奇点结构或晚时渐近构造时空的结果。建立了爱因斯坦方程一般宇宙学解的渐近行为的猜想图。与主题相关的一些杂项主题收集在单独的部分中。