This volume contains previously unpublished papers on algebraic K -theory written by Leningrad mathematicians over the last few years. The main topic of the first part is the computation of K -theory and K -cohomology for special varieties, such as group varieties and their principal homogeneous spaces, flag fiber bundles and their twisted forms, lambda -operations in higher K -theory, and Chow groups of nonsingular quadrics. The second part deals with Milnor K -theory: Gersten's conjecture for K^M_3 of a discrete valuation ring, the absence of p -torsion in K^M_* for fields of characteristic p , Milnor K -theory and class field theory for multidimensional local fields, and the triviality of higher Chern classes for the K -theory of global fields.