He was born in Shatura, near Moscow. He received his Ph.D. from Moscow State University under the direction of Lev Pontryagin, and then became a professor at this university. He died in Moscow.

• Fundamentals of Galois theory, 1961; 142 pp. Dover reprint, 2004
• The variational theory of geodesics, Translated from the Russian by Scripta Technica, Inc. Edited by Bernard R. Gelbaum. Saunders, Philadelphia, Pa., 1967; 200 pp.^[1]
• Linear algebra and differential geometry. Translated from the Russian by Vladimir Shokurov. Mir Publishers, 1982; 319 pp.
• Smooth manifolds, Mir Publishers, 1989; 511 pp.
• Geometry VI: Riemannian Geometry, Springer, 2001, 504 pp.

French edit

• Leçons de géométrie : Semestre I : Géométrie analytique, Éditions Mir, 1981; 279 pp.
• Leçons de géométrie : Semestre II : Algèbre linéaire et géométrie différentielle, Éditions Mir, 1981; 263 pp.
• Leçons de géométrie : Semestre III : Variétés différentiables, Éditions Mir, 1990; 431 pp.
• Leçons de géométrie : Semestre IV : Géométrie différentielle, Éditions Mir, 1990; 439 pp.
• Leçons de géométrie : Semestre V : Groupes et algèbres de Lie, Éditions Mir, 1985; 374 pp.

• Postnikov system
• Postnikov square

• O'Connor, John J.; Robertson, Edmund F., "Mikhail Mikhailovich Postnikov", MacTutor History of Mathematics Archive, University of St Andrews
• Postnikov, M. M. (1993), "Pages of a mathematical autobiography (1942--1953)", in Zdravkovska, Smilka; Duren, Peter L. (eds.), Golden years of Moscow mathematics, Hist. Math., vol. 6, Providence, R.I.: American Mathematical Society, pp. 155–178, ISBN 978-0-8218-9003-5, MR 1246563
• Rudyak, Yuli (2009), "M. M. Postnikov: his life, work and legacy", Algebraic topology---old and new, Banach Center Publications, vol. 85, Polish Acad. Sci. Inst. Math., Warsaw, pp. 15–29, doi:10.4064/bc85-0-1, ISBN 978-83-86806-04-1, MR 2503515