This book divides into three parts. Part I develops the mathematical tools used in the general theory of relativity. Since I wanted to keep this part short, but reasonably self-contained, I have adopted the dry style of most modern mathematical texts. Readers who have never before been confronted with differential geometry will find the exposition too abstract and will miss motivations of the basic concepts and constructions. In this case, one of the suggested books in the reference list should help to absorb the material. I have used notations as standard as possible. A collection of important formulae is given at the end of Part I. Many readers should start there and go backwards, if necessary.

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