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 Editorial 251 Algebraic construction and properties of hermitian analogs of $K$-theory over rings with involution from the viewpoint of hamiltonian formalism. applications to differential topology and the theory of characteristic classes. IS. P. Novikov 253 A new construction in the theory of lattice coverings of an $n$-dimensional space by equal spheresB. N. Delone, N. P. Dolbilin, S. S. Ryshkov, M. I. Shtogrin 289 Sums of characters over prime numbersA. A. Karatsuba 299 Cohomology of the Lie algebra of formal vector fieldsI. M. Gel'fand, D. B. Fuchs 322 Analogs of Torelli's theorem for multidimensional vector bundles over an arbitrary algebraic curveA. N. Tyurin 338 On the question of the structure of the subfield of invariants of a cyclic group of automorphisms of the field $\mathbf Q(x_1,…,x_n)$V. E. Voskresenskii 366 On the problem of a finite basis of identities in groupsA. Yu. Ol'shanskii 376 On the classification of simple Lie algebras over a field of nonzero characteristicV. G. Kac 385 Isogenies and torsion of elliptic curvesA. N. Parshin 409 Variational methods in nonstationary problems (parabolic case)P. P. Mosolov 425 Stability tests for the solutions of linear operator equations with discrete and continuous lags in the argumentsZ. I. Rekhlitskii 458