The main subject of this book is an up-to-date and in-depth survey of the theory of normal frames and coordinates in di?erential geometry. The existing results, as well as new ones obtained lately by the author, on the theme are presented. The text is so organized that it can serve equally well as a reference manual, introduction to and review of the current research on the topic. Correspondingly, the possible audience ranges from graduate and post-graduate students to sci- tists working in di?erential geometry and theoretical/mathematical physics. This is re?ected in the bibliography which...