On invariant linear connections. (Russian) Dokl. Akad. Nauk SSSR 128, 653-654 (1959).

Homogeneous cones. (Russian) Dokl. Akad. Nauk SSSR 133, 9-12 (1960); English transl.: Sov. Math., Dokl. 1, 787-790 (1960).

Invariant linear connections in a homogeneous space. (Russian) Trudy Mosk. Mat. Obshch. 9, 191-210 (1960).

The Morozov-Borel theorem for real Lie groups. (Russian) Dokl. Akad. Nauk SSSR 141, 270-273 (1961); English transl.: Sov. Math., Dokl. 2, 1416-1419 (1961).

Convex homogeneous domains. (Russian) Dokl. Akad. Nauk SSSR 141, 521-524 (1961); English transl.: Sov. Math., Dokl. 2, 1470-1473 (1961);

Lie groups and homogeneous spaces. (Russian) Itogi Nauki, Algebra, Topologiya, 5-32 (1962).

Automorphisms of homogeneous convex cones. (Russian) Dokl. Akad. Nauk SSSR 143, 265-268 (1962); English transl.: Sov. Math., Dokl. 3, 371-374 (1962).

The theory of convex homogeneous cones. (Russian) Trudy Mosk. Mat. Obshch. 12, 303-358 (1963); English transl.: Trans. Mosc. Math. Soc. 1963, 340-403 (1965).

(with Gindikin, S.G. and Pyateckij-Shapiro, I.I.) Classification and canonical realization of complex bounded homogeneous domains. (Russian) Trudy Mosk. Mat. Obshch. 12, 359-388 (1963); English transl.: Trans. Mosc. Math. Soc. 1963, 404-437 (1965).

The structure of the group of automorphisms of a homogeneous convex cone. (Russian) Tr. Moskov. Mat. Obsc. 13, 56-83 (1965); English transl.: Trans. Moscow Math. Soc. 13(1965), 63-93 (1967).

On a theorem on the infinite dimensionality of an associative algebra. (Russian) Izv. Akad. Nauk SSSR, Ser. Mat. 29, 209-214 (1965); English transl.: Amer. Math. Soc., Transl., II. Ser. 82, 237-242 (1969).

A construction of the exceptional simple Lie algebras. (Russian) Tr. Semin. Vektorn. Tenzorn. Anal. Prilozh. Geom. Mekh. Fiz. 13, 7-9 (1966); English transl. in: Vinberg, E. B. (ed.): Lie Groups and Invariant Theory. Providence, RI: American Mathematical Society. Transl. Ser. 2, 2005, v. 213, 29-30.

(with Andreev, E.M. and Ehlashvili, A.G.) Orbits of greatest dimension of semisimple linear Lie groups. (Russian) Funkts. Anal. Prilozh. 1, No.4, 3-7 (1967); English transl.: Funct. Anal. Appl. 1, 257-261 (1967).

Discrete groups generated by reflections in Lobachevsky spaces. (Russian) Mat. Sb., n. Ser. 72(114), 471-488, 73(115), 303 (1967); English transl.: Math. USSR Sb. 1, 429-444 (1967).

(with Gindikin, S.G.) K\«ahler manifolds admitting a transitive solvable group of automorphisms. (Russian) Mat. Sb., n. Ser. 74(116), 357-377 (1967); English transl.: Math. USSR Sb. 3, 333-351 (1967).

(with Kac, V.G.) Quasi-homogeneous cones. ( Russian) Mat. Zametki 1, 347-354 (1967); English transl.: Math. Notes 1, 231-235 (1967).

Compact Lie groups. (Russian) Moskva: Izdatel'stvo Moskovskogo Universiteta. 86p. (1967).

Invariant norms in compact Lie algebras. (Russian) Funkts. Anal. Prilozh. 2, No.2, 89-90 (1968); English transl.: Funct. Anal. Appl. 2, 177-179 (1968).

(with Gindikin, S.G. and Pjateckii-Shapiro, I.I.) Homogeneous K\»ahler manifolds. C.I.M.E., 3. Ciclo 1967, Geom. homogen. bounded domains, 1-87 (1968).

Some examples of crystallographic groups in Lobachevsky spaces. (Russian) Mat. Sb., n. Ser. 78(120), 633-639 (1969); English transl.: Math. USSR, Sb. 7, 617-622 (1969).

(with Onishchik, A.L.) Seminar on algebraic groups and Lie groups. (Russian) Moskva: Moskovskii Gosudarstvennyi Universitet, 230p. (1969).

Geometric represenations of Coxeter groups. (Russian) Usp. Mat. Nauk 25, No.2(152), 267-268 (1970).

Rings of definition of dense subgroups of semisimple linear groups. (Russian) Izv. Akad. Nauk SSSR, Ser. Mat. 35, 45-55 (1971); English transl.: Math. USSR, Izv. 5(1971), 45-55 (1972).

Diskrete linear groups generated by reflections. (Russian) Izv. Akad. Nauk SSSR, Ser. Mat. 35, 1072-1112 (1971); English transl.: Math. USSR, Izv. 5(1971), 1083-1119 (1972).

On the unit groups of some quadratic forms. (Russian) Mat. Sbornik, n. Ser. 87(129), 18-36 (1972); English transl.: Math. USSR, Sbornik 16, 17-35 (1972).

Algebraic transformation groups of maximal rank. (Russian) Mat. Sbornik, n. Ser. 88(130), 493-503 (1972); English transl.: Math. USSR, Sbornik 17(1972), 487-496 (1973).

On unimodular integral quadratic forms. (Russian) Funkts. Anal. Prilozh. 6, No.2, 24-31 (1972); English transl.: Funct. Anal. Appl. 6, 105-111 (1972).

(with Popov, V.L.) On a class of quasihomogeneous affine varieties. (Russian) Izv. Akad. Nauk SSSR, Ser. Mat. 36, 749-764 (1972); English transl.: Math. USSR, Izv. 6(1972), 743-758 (1973).

(with Gufan, Ju.M., Sahnenko, V.P., and Sirotin, Ju.I.) Symmetry change in crystals with space group $O^1_h$ during phase transitions (Russian) Kristallografiya 19, 21-26 (1974); English transl.: Sov. Phys., Crystallogr. 19, 10-13 (1974).

On the Sch\«onflies-Bieberbach theorem. (Russian) Doklady Akad. Nauk SSSR 221, 1013-1015 (1975); English transl.: Soviet Math., Doklady 16, 440-442 (1975).

On the linear groups associated to periodic automorphisms of semisimple algebraic groups. (Russian) Dokl. Akad. Nauk SSSR 221, 767-770 (1975); English transl.: Sov. Math., Dokl. 16, 406-409 (1975).

Some properties of the root decomposition of a semisimple Lie algebra over an algebraically nonclosed field. (Russian) Funkts. Anal. Prilozh. 9, No.1, 20-24 (1975); English transl.: Funct. Anal. Appl. 9, 17-21 (1975).

Some arithmetical discrete groups in Lobachevsky spaces. Discrete Subgroups of Lie Groups Appl. Moduli, Pap. Bombay Colloq. 1973, 323-348 (1975).

On the classification of the nilpotent elements of graded Lie algebras. (Russian) Dokl. Akad. Nauk SSSR 225, 745-748 (1975); English transl.: Sov. Math. Dokl. 16(1975), 1517-1520 (1976).

The Weyl group of a graded Lie algebra. (Russian) Izv. Akad. Nauk SSSR, Ser. Mat. 40, 488-526 (1976). English transl.: Math. USSR, Izv. 10(1976), 463-495 (1977).

(with Kac, V.G. and Popov, V.L.) Sur les groupes lin\'eaires alg\'ebriques dont l'alg\`ebre des invariants est libre. C. r. Acad. Sci., Paris, Ser. A 283, 875-878 (1976).

(with Ehlashvili, A.G.) The classification of three-vectors of the nine-dimensional space. (Russian) Tr. Semin. Vektorn. Tenzorn. Anal. Prilozh. Geom. Mekh. Fiz. 18, 197-233 (1978); English transl.: Sel. Math. Sov. 7, No.1, 63-98 (1988).

(with Kac, V.G.) Spinors of 13-dimensional space. Adv. Math. 30, 137-155 (1978).

(with Kaplinskaja, I.M.) On the groups $O_{18,1}(\Bbb Z)$ and $O_{19,1}(\Bbb Z).$ (Russian) Dokl. Akad. Nauk SSSR 238, 1273-1275 (1978); English transl.: Sov. Math., Dokl. 19, 194-197 (1978).

(with Kimel'fel'd, B.N.) Homogeneous domains on flag manifolds and spherical subgroups of semisimple Lie groups. (Russian) Funkts. Anal. Prilozh. 12, No.3, 12-19 (1978); English transl.: Funct. Anal. Appl. 12, 168-174 (1979).

(with Shvartsman, O.V.) Riemannian surfaces. (Russian) Itogi Nauki Tekh., Ser. Algebra Topolo\-gija Geom. 16, 191-245 (1978); English transl.: J. Sov. Math. 14, 985-1020 (1980).

A classification of homogeneous nilpotent elements of a semisimple graded Lie algebra. (Russian) Tr. Semin. Vektorn. Tenzorn. Anal. Prilozh. Geom. Mekh. Fiz. 19, 155-177 (1979); English transl.: Sel. Math. Sov. 6, 15-35 (1987).

On the closure of an orbit of a reductive linear group. (Russian) Algebra, Collect., Moskva 1980, 31-36 (1980).

Invariant convex cones and orderings in Lie groups. (Russian) Funkts. Anal. Prilozh. 14, No.1, 1-13 (1980); English transl.: Funct. Anal. Appl. 14, 1-10 (1980).

Algebra of polynomials. Textbook. (Russian) Ministerstvo Prosveshcheniya RSFSR. Moskovskij Gosudarstvennyj Zaochnyj Pedagogicheskij Institut. Moskva: «Prosveshchenie». 176 p. (1980).

Absence of crystallographic reflection groups in Lobachevsky spaces of large dimension. (Russian) Funkts. Anal. Prilozh. 15, No.2, 67-68 (1981); English transl.: Funct. Anal. Appl. 15, 128-130 (1981).

Rationality of the field of invariants of a triangular group. (Russian) Vestn. Mosk. Univ., Ser. I 1982, No.2, 23-24 (1982); English transl.: Mosc. Univ. Math. Bull. 37, No.2, 27-29 (1982).

Effective theory of invariants. (Russian) Algebra, Work Collect., dedic. O. Yu. Shmidt, Moskva 1982, 27-33 (1982); English transl.: Transl., II. Ser., Am. Math. Soc. 137, 15-19 (1987).

On reflective hyperbolic lattices. (Russian) Dokl. Akad. Nauk SSSR 272, 1298-1301 (1983); English transl.: Sov. Math., Dokl. 28, 517-520 (1983).

(with Artamonov, V.A. et al.) Practical studies on algebra. (Russian) Moskva: Izdatel'stvo Moskovskogo Universiteta. 92 p. (1983).

Discrete reflection groups in Lobachevsky spaces of high dimension. (Russian) Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 132, 62-68 (1983); English transl.: J. Sov. Math. 30, 1837-1841 (1985).

The two most algebraic K3 surfaces. Math. Ann. 265, 1-21 (1983).

The non-existence of crystallographic groups of reflections in Lobachevsky spaces of large dimension. (Russian) Tr. Mosk. Mat. O-va 47, 68-102 (1984); English transl.: Trans. Mosc. Math. Soc. 1985, 75-112 (1985).

Discrete reflection groups in Lobachevsky spaces. Proc. Int. Congr. Math., Warszawa 1983, Vol. 1, 593-601 (1984).

Hyperbolic reflection groups. (Russian) Usp. Mat. Nauk 40, No.1(241), 29-66 (1985); English transl.: Russ. Math. Surv. 40, No.1, 31-75 (1985).

Linear representations of groups. (Russian) Moskva: «Nauka». Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 144 p. (1985); English transl.: Basler Lehrb\»ucher, 2. Basel etc.: Birkh\«auser Verlag. 146 p. (1989).

Complexity of actions of reductive groups. (Russian) Funkts. Anal. Prilozh. No.1, 1-13 (1986); English transl.: Funct. Anal. Appl. 20, 1-11 (1986).

(with Artamonov, V.A. et al.) A collection of problems on algebra. Textbook. (Russian) Ed. by A. I. Kostrikin. Moskva: ``Nauka''. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 352 p. R. 1.00 (1987); English transl.: Algebra, Logic and Appl. Ser, vol. 6. Gordon and Breach Publishers, 464 p. (1996).

Reflection subgroups in Bianchi groups. (Russian) Vopr. Teor. Grupp Gomologicheskoj Algebry 7, 121-127 (1987); English transl.: Sel. Math. Sov. 9, No.4, 309-314 (1990).

(with Shvartsman, O.V.) Discrete groups of motions of spaces of constant curvature. (Russian) Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 29, 147 - 259 (1988); English transl.: Geometry II. Encycl. Math. Sci. 29, 139-248 (1993).

(with Alekseevskij, D.V. and Solodovnikov, A.S.) Geometry of spaces of constant curvature. (Russian) Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 29, 5-146 (1988); English transl.: Geometry II. Encycl. Math. Sci. 29, 1-138 (1993).

(with Onishchik, A.L.) Foundations of the theory of Lie groups. (Russian) Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 20, 5-101 (1988); English transl.: Lie groups and Lie algebras I. Encycl. Math. Sci. 20, 1-94 (1993).

(with Gorbatsevich, V.V. and Shvartsman, O.V.) Discrete subgroups of Lie groups. (Russian) Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 21, 5-120 (1988); English transl.: Lie groups and Lie algebras II. Encycl. Math. Sci. 21, 1-123 (2000).

(with Onishchik, A.L.) Seminar on Lie groups and algebraic groups. (Russian) Moskva: Nauka. 344 p.(1988); English transl.: Lie groups and algebraic groups. Springer Series in Soviet Mathematics. Berlin etc.: Springer-Verlag, xvii, 328 p. (1990).

Real entire functions with prescribed critical values. (Russian) Vopr. Teor. Grupp Gomologicheskoj Algebry 9, 127-138 (1989).

(with Popov, V.L.) Invariant theory. (Russian) Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 55, 137-309 (1989); English transl.: Algebraic geometry IV. Encycl. Math. Sci. 55, 123-278 (1994).

On certain commutative subalgebras of the universal enveloping algebra. (Russian) Izv. Akad. Nauk SSSR, Ser. Mat. 54, No.1, 3-25 (1990); English transl.: Math. USSR, Izv. 36, No.1, 1-22 (1991).

(with Gorbatsevich, V.V. and Onishchik, A.L.) Structure of Lie groups and algebras. (Russian) Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 41, 259 p. (1990); English transl.: Lie groups and Lie algebras III. Encyclopaedia of Mathematical Sciences. 41. Berlin: Springer-Verlag, 248 p. (1994).

The volume of polyhedra on a sphere and in Lobachevsky space. Transl., Ser. 2, Am. Math. Soc. 148, 15-27 (1991).

(with Popov, V.L.) Some open problems in invariant theory. Algebra, Proc. Int. Conf. Memory A. I. Mal'cev, Novosibirsk/USSR 1989, Contemp. Math. 131, Pt. 3, 485-497 (1992).

Volumes of non-Euclidean polyhedra. (Russian) Usp. Mat. Nauk 48, No.2(290), 17-46 (1993); English transl.: Russ. Math. Surv. 48, No.2, 15-45 (1993).

The smallest field of definition of a subgroup of the group $PSL(2,C)$. (Russian) Mat. Sb. 184, No.10, 53-66 (1993); English transl.: Sb. Math. 80, No.1, 179-190 (1995).

Generalized derivations of algebras. Bokut', L. A. et al. (eds.), Third Siberian school on algebra and analysis. Proceedings of the third Siberian school, Irkutsk State University, Irkutsk, Russia, August 30-September 4, 1989. Providence, RI: American Mathematical Society, Transl., Ser. 2, Am. Math. Soc. 163, 185-188 (1995).

The asymptotic semigroup of a semisimple Lie group. Hofmann, Karl Hofmann et al. (eds.): Semigroups in algebra, geometry and analysis. Berlin: de Gruyter . De Gruyter Expo. Math. 20, 293-310 (1995).

(with Karpelevich, F.I. and Onishchik, A.L.) On the work of E.B.Dynkin in the theory of Lie groups. Gindikin, S. G. et al. (eds.): Lie groups and Lie algebras: E.B.Dynkin's seminar. Providence, RI: American Mathematical Society. Transl. Ser. 2, Am. Math. Soc. 169, 1-13 (1995).

On reductive algebraic semigroups. Gindikin, S. G. et al. (eds.): Lie groups and Lie algebras: E.B.Dynkin's seminar. Providence, RI: American Mathematical Society. Transl. Ser. 2, Am. Math. Soc. 169, 145-182 (1995).

(with Mennicke, J. and Helling, H.) On some generalized triangle groups and three-dimensional orbifolds. (Russian) Tr. Mosc. Mat. O-va 56, 5-32 (1995); English transl.: Trans. Mosc. Math. Soc. 1995, 1-21 (1995).

On invariants of a set of matrices. Journal of Lie Theory 6, No.2, 249-269 (1996).

Groups defined by periodic paired relations. (Russian) Mat. Sb., 188, No.9, 3-12 (1997); English transl.: Sb. Math. 188, No.9, 1269-1278 (1997).

Invariants of 2×2 matrices. Preprint 97-084, Universit\»at Bielefeld, 16 p. (1997).

On limits of algebraic subgroups. Vestnik Tambovskogo universiteta 2, No.4, 420-427 (1997).

Classification of 2-reflective hyperbolic lattices of rank 4. Preprint 98-113, Universit\«at Bielefeld, 35 p. (1998).

(with Akhiezer, D. N.) Weakly symmetric spaces and spherical varieties. Transformation Groups 4, No.1, 3-24 (1999).

(with Panyushev, D. I.) An infinitesimal characterization of the complexity of homogeneous spaces. Transformation Groups 4, No.1, 97-101 (1999).

A course in algebra. (Russian) Moskva: Faktorial, 528 p. (1999); Second edition, revised and expanded: Moskva: Faktorial, 543 p. (2001). Third edition, revised and expanded: Moskva: Faktorial, 544 p. (2002). Fourth edition, revised and expanded: Moskva: MCCME, ??? p. (2010).

(with Kaplinsky, Y.) Pseudo-finite generalized triangle groups. Preprint 00-003, Universit\»at Bielefeld, 28 p. (2000).

On stability of actions of reductive algebraic groups. Fong, Y., Mikhalev, A. A., Zelmanov, E. (eds.): Lie Algebras, Rings and Related Topics, Springer-Verlag, 188-202 (2000).

(with Margulis, G.A.) Some linear groups virtually having a free quotient. Journal of Lie Theory 10, No.1, 171-180 (2000).

Commutative homogeneous spaces and coisotropic symplectic actions. (Russian) Uspekhi Mat. Nauk 56, No.1, 3-62 (2001).

Equivariant symplectic geometry of cotangent bundles. Moscow Math. J. 1, No.2, 287-299 (2001).

(with Noskov, G.A.) Strong Tits alternative for subgroups of Coxeter groups. Journal of Lie Theory 12, No.1, 259-264 (2002).

(with Hilgert, J. and Pasquale, A.) The dual horospherical Radom trasform for polynomials. Moscow Math. J. 2, No.1, 113-126 (2002).

Kaleidoscopes and reflection groups.(Russian) Matem. Prosveshch. 7, 45-63 (2003).

Commutative homogeneous spaces of Heisenberg type. (Russian) Trudy Mosk. Mat. Obshch. 64, 54-89 (2003).

(with Hilgert, J. and Pasquale, A.) The dual horospherical Radon transform as a limit of spherical Radon transforms, Amer. Math. Soc. Transl. 210, 135-143 (2003).

(with Potyagailo, L.) On right-angled reflection groups in hyperbolic spaces, Comment. Math. Helv., 80, 63-73 (2005).

Short $\text{SO}_3$-structures on simple Lie algebras and the associated quasielliptic planes. Vinberg, E. B. (ed.): Lie Groups and Invariant Theory. Providence, RI: American Mathematical Society. Transl. Ser. 2, v. 213, 1-28 (2005).

Classification of 2-reflective hyperbolic lattices of rank 4. (Russian) Trudy Mosk. Mat. Obshch. 68, 44-76 (2007).

On abelian coverings of surfaces, Michigan Math. J. 55, No.3 (2007).

On some number-theoretic conjectures of V.Arnold, Japan. J. Math. 2, 297-302 (2007).

(with Kapovich, M. and Potyagailo, L.) Non-coheremce of some lattices in $Isom(H^n)$. In: Geometry \& Topology Monographs 14 a volume in memory of H.Zieschang, 335-351 (2008).

Wonderful arithmetic properties of binomial coefficients. (Russian) Matem. Prosveshch. 12, 33-42 (2008).

Fermat's little theorem and generalizations. (Russian) Matem. Prosveshch. 12, 43-54 (2008).

(with Elashvili, A.G. and Kac, V.G.) On exceptional nilpotents in semisimple Lie algebras. J. Lie Theory 19, No.2, 371-390 (2009).

(with Khoroshkin, S. and Nazarov, M.) A generalized Harish-Chandra isomorphism. Adv. Math. 226, 1168-1180 (2011). (Available online 24 August 2010.)

(with Abels, H.) Generating simple groups by tori. J.Algebra 328, 114-121 (2011) (Available online 1 June 2010)

On automorphic forms on symmetric domains of type IV. (Russian) Uspekhi Mat. Nauk 65, No.2, 94-95 (2010).

Some free algebras of automorphic forms on symmetric domains of type IV. Transformation Groups 15, No.3, 701-741 (2010).

(with Elashvili, A. and Jibladze, M.) Moduli algebras of some simplest non-semiquasihomogeneous singularities.

(with Elashvili, A.G. and Kac, V.G.) Cyclic elements in semisimple Lie algebras. Transformation Groups.

Some examples of Fuchsian groups sitting in SL_2(Q). Bielefeld University, SFB 701, Preprint 12011.