An explication of the principles and methods of differential geometry. Beginning at an introductory level with curves in Euclidean space, the sections become increasingly more challenging, arriving at such advanced topics as transformation groups, the equivalence problem, and elliptical operators. The idea is that readers at different levels can come on board when it stops being facile, and bail out when it stops being comprehensible. First published in Russian, 1988. Annotation copyright Book News, Inc. Portland, Or.