Includes bibliographical references.

On the congruence problem for linear groups over arithmetic rings;Birational properties of the reduced Whitehead group;Projective modules over group rings of nilpotent groups;On torsion in higher Milnor functors for multidimensional local fields; theory of Demazure models;Norms in fields of real algebraic functions, and the reduced Whitehead group;The reduced Whitehead group of weakly and totally ramified division algebras;The structure of unitary and orthogonal groups over Henselian discretely normed Azumaya algebras;Reduced unitary Whitehead groups and noncommutative rational functions;Rational splitting fields of simple algebras and unirationality of conic bundles;Crossed products of simple algebras and their automorphism groups;On the metaplectic kernel for anisotropic groups;The metaplectic kernel for the group L(1,D) On finite presentability of reduced norms in simple algebras;Unitarity of the multiplicative group of a group algebra;Profinite completions of linear solvable groups;On the Grothendieck and Platonov conjectures;The congruence problem for solvable algebraic groups over global fields of positive characteristic; theory of free products and the Bass problem;On a theorem of Gersten for graded rings;Algebraic theory of Banach algebras;On the finite generation of the character ring of three-dimensional unimodular group representations;The _G functor on the category of inverse spectra of topological spaces; theory on the category of distributive lattices; theory on the category of topological spaces; theory on the category of Boolean algebras with closure;On index theory for a family of Fredholm complexes;On noncommutative function spaces;Generalized resolvents of nondensely defined bounded symmetric operators