Differential geometry rests on the twin pillars of linear algebra‐multilinear algebra and topology‐analysis. Part I of the book provides an overview of selected topics from these areas of mathematics. Most of the linear algebra presented here is likely familiar to the reader, but the same may not be true of the multilinear algebra, with the exception of the material on determinants. Topology and analysis are vast subjects, and only the barest of essentials are touched on here. In order to keep the book to a manageable size, not all theorems are provided with a proof, a remark that also applies to Part II and Part III.