This volume contains previously unpublished papers on algebraic $K$-theory written by Leningrad mathematicians over the last few years.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.