Victor Borisovich Lidskii (1924-2008);In memory of Victor Borisovich Lidskii (1924-2008);List of publications by V. B. Lidskii;Eigenvalue inequalities for mixed Steklov problems;The analog of the limiting absorption principle in homogenization of periodic elliptic operators;On a class of nonselfadjoint periodic boundary value problems with discrete real spectrum;Spectral instability of semiclassical operators;Estimates of solutions to some weighted systems defined on mathbb {R}^N On guided electromagnetic waves in photonic crystal waveguides;Spectral inequalities for a class of nonellilptic operators;On the near periodicity of eigenvalues of Toeplitz matrices;Green's kernels for transmission problems in bodies with small inclusions;Lower bound on the density of states for periodic Schr�odinger operators;On some open problems in spectral theory