Kostrikin graduated from the Faculty of Mechanics and Mathematics at Moscow State University in 1952. In 1960, he earned a Doctor of Sciences degree under Igor Shafarevich at the Steklov Institute of Mathematics with a thesis on the Burnside problem. He became a faculty member at Moscow State University in 1963 and became a professor at the same university in 1976. In 1998, he became Honoured Professor of Moscow State University.
- Around Burnside, Springer Verlag 1990 2012 pbk reprint
- with Pham Huu Tiep: Orthogonal Decompositions and Integral Lattices, de Gruyter 1994
- with Yuri Manin: Linear algebra and geometry, Gordon and Breach 1989; 1997 pbk edition
- Introduction to Algebra, Springer Verlag 1982 (Russian original 1977)
- Exercises in algebra: a collection of exercises in algebra, linear algebra and geometry, Gordon and Breach 1996
- V. A. Artamonov, Yu. A .Bahturin, I. A. Chubarov, et al., Dedication: Alexei Ivanovich Kostrikin, Comm. Algebra 29 (9) (2001), ix–xiv.
- Preface: On the 70th birthday of Alexei Ivanovich Kostrikin, J. Math. Sci. (New York) 93 (6) (1999), 801–808.
- E. B. Vinberg, E. S. Golod, E. I. Zelmanov, et al., Aleksei Ivanovich Kostrikin [1929–2000] (Russian), Uspekhi Mat. Nauk 56 3(339) (2001), 143–145.
- E. B. Vinberg, E. S. Golod, E. I. Zelmanov, et al., Aleksei Ivanovich Kostrikin [1929–2000], Russian Math. Surveys 56 (3) (2001), 559–561.
- Alexei Kostrikin at the Mathematics Genealogy Project
- Newman, M. F.; Wall, G. E. (1993). "Book Review: Around Burnside by A. I. Kostrikin and The restricted Burnside problem by Michael Vaughan-Lee". Bulletin of the American Mathematical Society. 28 (1): 157–162. doi:10.1090/S0273-0979-1993-00341-0. ISSN 0273-0979.
- Tobin, Seán (1993). "Review of Around Burnside by A. I. Kostrikin, translated from the Russian by James Wiegold" (PDF). IMS Bulletin. 31: 68–74.
- Howie, J. M. (1983). "Review of Introduction to algebra by A. I. Kostrikin, translated by N. Koblitz". Proceedings of the Edinburgh Mathematical Society. 26 (3): 401.
- O'Connor, John J.; Robertson, Edmund F., "Aleksei Ivanovich Kostrikin", MacTutor History of Mathematics archive, University of St Andrews.