Аннотация:

In the paper is given a survey of publications by Yu.F. Borisov. Also we present some  information and results on two-dimensional manifolds of bounded curvature in the sense of A.D. Alexandrov, metric foundations of Riemannian geometry, and Busemann spaces, connected by the subject with  publications and problems of Borisov. At the end, we cite some  reminiscences of A.D. Alexandrov, Yu.F. Borisov, N.V. Efimov, Yu.G. Reshetnyak.