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 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整体动力学定理。

本文是关于爱因斯坦方程解的存在性和整体动力学定理的指南。它引起了人们对该领域未解决问题的关注。调查了相对较容易理解的本地实时柯西问题。讨论了具有各种对称类型的解决方案的整体结果。提出了牛顿理论和狭义相对论的一些结果，它们提供了有用的比较。给出了在小数据情况下的全局结果的处理以及具有规定奇异性结构的时空构造的结果。建立了一个关于爱因斯坦方程的一般宇宙学解的渐近行为的猜想图。在单独的部分中收集了与主要主题相关的一些其他主题。