In this text the author looks at the work of Riemann, who in the 19th century contributed to the study of curved surfaces, or non-Euclidian geometry. Riemann's results later found application in physics, when Einstein introduced his theory of relativity. "Eisenhart's classic work on the application of tensor calculus to geometry was originally published in 1926 . . . It is still one of the best accounts of the subject."---E. J. F. Primrose, Mathematical Gazette