  This book is expository and is in Russian (sample English translation of two
pages is given). It is shown how in the course of solution of interesting
geometric problems (close to applications) naturally appear different notions
of curvature, which distinguish given geometry from the 'ordinary' one. Direct
elementary definitions of these notions are presented. The book is accessible
for students familiar with analysis of several variables, and could be an
interesting easy reading for professional mathematicians. The material is
presented as a sequence of problems, which is peculiar not only to Zen
monasteries but also to serious mathematical education.
