Burago studied at Leningrad University, where he obtained his Ph.D. and Habilitation degrees.

Yuri is a creator (with his students Perelman and Petrunin, and M. Gromov) of what is known now as Alexandrov Geometry.

Burago is the head of the Laboratory of Geometry and Topology that is part of the St. Petersburg Department of Steklov Institute of Mathematics.

[4] His other books and papers include: He has advised Grigori Perelman, who solved the Poincaré conjecture, one of the seven Millennium Prize Problems.

Burago was an advisor to Perelman during the latter's post-graduate research at St. Petersburg Department of Steklov Institute of Mathematics.