Troitsk: Troitsk branch of the state educational institution of higher professional education "Chelyabinsk State University", 2012. 104 s. 2nd Edition . , spr. and dop. This manual is the first part of the course Functional analysis devoted to the study of the general and basic properties of metric spaces. The structure of this manual and all subsequent ones is as follows: theoretical information, examples of solving problems related to this theory, as well as problems for independent solving. The manual presents theoretical and practical material on the topic "Metric spaces", studied by students of the specialty "Applied mathematics and computer science" . The manual is distinguished by a summary brevity and simplicity of presentation . The solution of the most complex problems is given as examples, to many problems for independent solution are given instructions. The training manual is intended for teachers and students. Can be used to conduct practical classes and organize independent work of students.