On the scientific work of M. Sh. Birman in 1998-2007;Continuation of the list of publications of M. Sh. Birman;Perturbations of the continuous spectrum of a singular elliptic operator by varying the boundary and the boundary conditions;Asymptotic behavior of the eigenfunctions of many-particle Schr�odinger operator. I. One-dimensional particles;Spectral asymptotics of the Maxwell operator on Lipschitz manifolds with boundary;Spectral inequalities for Schr�odinger operators with surface potentials;On the spectrum of the Dirichlet Laplacian in a narrow infinite strip;Lyapunov functions of periodic matrix-valued Jacobi operators;Hardy inequalities for simply connected planar domains;The spectral flow, the Fredholm index, and the spectral shift function;On the spectrum of a translationally invariant Pauli operator;Discrete spectrum distribution of the Landau operator perturbed by an expanding electric potential;On the comparison of the Dirichlet and Neumann counting functions;Absolutely continuous spectrum of multi-dimensional Schr�odinger operators with slowly decaying potentials;On the discrete spectrum of the perturbed periodic magnetic Schr�odinger operator with degenerate lower edge of the spectrum;Homogenization of periodic second order differential operators including first order terms;Improved Berezin-Li-Yau inequalities with a remainder term;Spectral and scattering theory of fourth order differential operators