Conference held at Akademgorodok, Novosibirsk, USSR, Aug. 2126, 1989.

Includes bibliographical references.

Groups associated with some types of infinitedimensional Lie algebras ; The method of classification of periodic words and the Burnside problem ; On Malcev's theorem on elementary equivalence of linear groups ; The Malcev correspondence revisited ; When is multiplication by a closed map? ; A maximal subgroup in the simple finite group _8(q) ; On group algebras with solvable unit groups ; The category of quasihomomorphisms of abelian torsion free groups of finite rank ; A generalization of Malcev's correspondence between rings and groups and a class of Lie groups ; Isomorphisms of the general linear group rm GL_n(R),\ ; n\geq 4 over an associative ring ; Fong's reduction, the correspondences of Brauer and Glauberman and Alperin's weight conjecture ; On quadratic equations in free groups ; On representations of finite groups over some factorial rings ; Some recent results on automorphism groups ; Some problems in free group rings ; Partial orders of the group of automorphisms of the real line ; The subgroup structure of the classical groups ; On the identities of representations of groups by triangular matrices over a commutative ring ; Chevalley groups and their unipotent subgroups ; Maximal subgroups of finite simple groups and their automorphism groups ; On extensions of a separable roup by a quasicyclic roup ; Exceptional simple Lie group _4 and spin representations ; Weak second order logic in group theory ; Abstract isomorphisms of algebraic solvable groups ; The isomorphism problem for finite group rings ; On representations of the braid groups by matrices ; On subgroups of free products of cyclics ; On a conjecture of Zassenhaus, and beyond ; On extensions of rm po roups ; On successive free central extensions of \gamma _n(R) groups ; On nontrivial factorisations of a onegenerated local formation of finite groups ; Some arithmetical properties of finite groups and their linear representations ; On groups with fan subgroups ; Minimal polynomials of elements of order in irreducible representations of Chevalley groups over fields of characteristic ; Wreath product and factorization of groups ; Bounded generation of normal and twisted Chevalley groups over the rings of ntegers ; On the weak approximation in algebraic groups ; Vertex stabilizers of symmetric graphs with projective subconstituents ; Automorphisms of group rings ; Automorphisms of the free group of rank two ; Group rings of locally finite groups and representation theory ; Open subgroups of free profinite products ; Addition to my talk at the conference ; On some classes of periodic rm FC roups ; Planes with nondivision coordinate rings ; Equivalence of homomorphisms of surface groups to free groups and some properties of imensional handlebodies ; Automorphism groups of free geometries ; Flat conformal structures on anifolds (survey) Eiichi Abe ; S I Adian and I G Lysionok ; C I Beidar and A V Mikhalev ; O V Belegradek ; K Benabdallah and A Mader ; A V Borovik ; Adalbert Bovdi ; A A Fomin ; Thomas A Fournelle and Kenneth W Weston ; I Z Golubchik ; P G Gres ; R I Grigorchuk and P F Kurchanov ; P M Gudivok ; C K Gupta ; Narain Gupta ; W Charles Holland ; Oliver King ; A N Krasilnikov ; V M Levchuk ; Martin W Liebeck and Jan Saxl ; A I Moskalenko ; Shingo Murakami ; A G Myasnikov and V N Remeslennikov ; K N Ponomaryov ; K W Roggenkamp ; V A Romankov ; Gerhard Rosenberger ; L L Scott ; E E Shirshova ; V E Shpilrain ; A N Skiba ; S P Strunkov ; I Ya Subbotin and N F Kuzennyi ; I D Suprunenko ; V I Suschansky ; O I Tavgen ; Nguy\cftilen Quoc Thang ; V I Trofimov ; D A R Wallace ; M J Wicks ; A E Zalesskii ; P A Zalesskii ; A Yu Ol'shanskii ; L A Kurdacenko ; John R Faulkner ; R I Grigorchuk P F Kurchanov and H Zieschang ; Oddvar Iden ; M E Kapovich