My research interests lie in the area of Groups, Rings, Lie and Hopf Algebras. The results obtained by me (often in cooperation with my colleagues) deal with the following matters:
 Identical relations and varieties of Lie and associative algebras and superalgebras,
 Enveloping algebras and representations of Lie algebras and superalgebras,
 Automorphism groups of certain Lie algebras,
 Structure and representations of locally finite Lie algebras,
 Algebras with actions and coactions of Hopf algebras,
 Graded algebras and applications.
I have written some monographs and textbooks (#3 below with my former students):
 Bahturin, J. A. Lectures on Lie algebras. Lectures given at Humboldt University, Berlin and Lomonosov University, Moscow. Studien zur Algebra und ihre Anwendungen [Studies in Algebra and its Applications], 4. AkademieVerlag, Berlin, 1978. viii+126 pp.
 Bahturin, Yu. A. Identical relations in Lie algebras. Translated from the Russian by Bakhturin. VNU Science Press, b.v., Utrecht, 1987. x+309 pp. ISBN: 9067640522
 Bahturin, Yuri A.; Mikhalev, Alexander A.; Petrogradsky, Viktor M.; Zaicev, Mikhail V. Infinitedimensional Lie superalgebras. de Gruyter Expositions in Mathematics, 7. Walter de Gruyter & Co., Berlin, 1992. x+250 pp. ISBN: 3110129744
 Bahturin, Yuri Basic structures of modern algebra. Mathematics and its Applications, 265. Kluwer Academic Publishers Group, Dordrecht, 1993. x+419 pp. ISBN: 0792324595
The most recent published papers include:
 Bahturin, Yuri.; Strade, Helmut. Locally finitedimensional simple Lie algebras. Mat. Sb. 185 (1994), no. 2, 332.
 Bahturin, Yuri.; Benkart, Georgia M.. Highest weight modules for locally finite Lie algebras. Modular interfaces...AMS/IP Studies in Math. 4 (1997), 131.
 Bahturin, Yuri.; Zaicev M. V. Identities of graded algebras. J. Algebra 205 (1998), no. 1, 112
 Bahturin, Yuri.; Linchenko, Vitaly. Identities of algebras with actions of Hopf algebras. J. Algebra, 202 (1998), 634  654.
 Bahturin, Yuri; Fischman, Davida; Montgomery, Susan. Bicharacters, twistings, and Scheunert's theorem for Hopf algebras. J. Algebra 236 (2001), no. 1, 246276.
 Bahturin, Yu. A.; Sehgal, S. K.; Zaicev, M. V. Group gradings on associative algebras. J. Algebra, 241 (2001), 677698.
