Differential Geometry Basic Notions and Physical Examples

“The book under review has grown out of lecture notes for a mini-course given at a workshop on differential geometry and continuum mechanics at the International Centre for Mathematical Sciences in 2013. … addressing researchers and engineers in particular, Epstein’s book provides a … quick way to appreciate modern differential geometry and topology and get to their essential ideas and usefulness. Surely, Epstein manages to give the reader a motivation to delve into the deep waters of these two fields.” (Theophanes Grammenos, Mathematical Reviews, June, 2015)

“This book is based on a short course on ‘Differential Geometry and Continuum Mechanics’ given by Marcelo Epstein at the International Centre of Mathematical Sciences in Edinburgh in June 2013. The course provided a guided tour of differential geometry for researchers and graduate students in science and engineering — many of whom had a particular interest in continuum mechanics. … this book is a gold mine of aesthetically pleasing mathematical ideas, the presentation of which is highly inspirational.” (P. N. Ruane, MAA Reviews, December, 2014)