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

Includes bibliographical references.

Combinatorial problems connected with finite homogeneity ; Lattices of conjugacy relations ; A categorical theorem on universal objects and its application in abelian group theory and computer science ; Minimal faithful permutation and transformation representations of groups and semigroups ; Free and finitely presented lattices ; On weak automorphisms of some finite algebras ; The Goldie dimension of some extensions of modular lattices ; A note on BarrDiaconescu covering theory ; On identities of cancellative semigroups ; On the ubiquity of Malcev operations ; Trees and inverse semigroups ; A "large" essentially minimal clone over an infinite set ; A characterization of decidable locally finite varieties ; A latticetheoretic characterization of equivalent quasivarieties ; Functionally complete and affine complete algebras and associated varieties ; Some algebraic aspects of database theory ; An introduction to the theory of modes and modals ; Locally residually finite and locally representable varieties of semigroups ; Hyperidentities and clone congruences ; Semigroup varieties with commuting fully invariant congruences on free objects ; Computer method in calculating unctions of nonisolated singularities ; The cone of effective divisors of threefolds ; Parametrization and embeddings of a class of homogeneous spaces ; The local uniformization of branches of an algebraic curve ; Analytic AxKochenErsov theorems ; Some examples of computation of a regulator map on singular varieties ; An intrinsic elimination theory by means of forms associated to algebraic varieties ; Boundedness of mathbf Q ano threefolds ; Weak approximation in algebraic groups and homogeneous spaces ; Diffeomorphism criteria for smooth manifolds and algebraic varieties ; Some aspects of computational algebraic number theory ; Localglobal principles in algebra and number theory ; Some open problems in invariant theory ; Positivity of sheaves and geometric invariant theory ; Complex divisors on algebraic curves and some applications to string theory ; Algebraic geometry via model theory ; Vector spaces with a distinguished subgroup ; A guided tour through nonstandard analysis ; Heytingvalued analysis: P. S. Novikov's hypotheses ; Definability and interpolation in classical modal logics ; Algebraic aspect of logics without structural rules ; Semantical significances of formulas in the classical predicate logic ; The universal theory of the free pseudoBoolean algebra _\omega (H) in the signature extended by constants for free generators ; Computing degrees of definable classes of sentences Gregory L Cherlin ; Stephen D Comer ; Manfred Droste and Rudiger Gobel ; David Easdown ; Ralph Freese ; Kazimierz Gazek ; Piotr Grzeszczuk ; George Janelidze ; Jan Krempa and Olga Macedonska ; J Lambek ; Stuart W Margolis and John C Meakin ; H Machida and I G Rosenberg ; Ralph McKenzie and Matthew A Valeriote ; Don Pigozzi ; Alden F Pixley ; B I Plotkin ; Anna Romanowska ; Mark V Sapir ; D Schweigert ; M V Volkov ; A G Aleksandrov and V L Kistlerov ; Victor V Batyrev ; Michel Brion ; A D Bruno and A Soleev ; Lou van den Dries ; Helene Esnault ; Federico Gaeta ; Yujiro Kawamata ; B E Kunyavskii and A N Skorobogatov ; Nikita Yu Netsvetaev ; M Pohst ; V Platonov ; V L Popov and E B Vinberg ; Eckart Viehweg ; Alexander A Voronov ; B I Zilber ; Steven Buechler ; A E Hurd ; V A Lyubetsky ; Larisa Maksimova ; Hiroakira Ono ; M G Peretyatkin ; V V Rybakov ; V L Selivanov