Alexandrov spaces are certain spaces that arise in differential geometry, named after Alexander Alexandrov. They should not be confused with Alexandroff spaces, which arise in general topology and are named after Paul Alexandroff.
Yukio Otsu, Differential geometric aspects of Alexandrov spaces, in: Comparison Geometry, MSRI publications 30, 1997. pdf
G. Perelman, Elements of Morse theory on Alexandrov spaces, SPb Math. J. 1994.
G. Perelman, DC structure on Alexandrov spaces, pdf
Yu. Burago, M. Gromov, G. Perelman, Alexandrov spaces with curvature bounded below, Russ. Math. Surveys 1992.
MathOverflow Details of Perelman’s example about soul of Alexandrov space, Metrically singular Alexandrov space, Is there Domain Invariance for Alexandrov spaces?, Rigidity of triangle comparison in Alexandrov spaces