0 Introduction -- 1 General Calculus of Pseudodifferential Operators -- 2 Model Classes of Degenerate Elliptic Differential Operators -- 3 General Classes of Degenerate Elliptic Differential Operators -- 4 Degenerate Elliptic Operators in Non - Power - Like Degeneration Case -- 5 Lp - Theory for Degenerate Elliptic Operators -- 6 Coersiveness of Degenerate Quadratic Forms -- 7 Some Classes of Hypoelliptic Pseudodifferential Operators on Closed Manifold -- 8 Algebra of Boundary Value Problems for Class of Pseudodifferential Operators which Change Order on the Boundary -- 9 General Schemes of Investigation of Spectral Asymptotics for Degenerate Elliptic Equations -- 10 Spectral Asymptotics of Degenerate Elliptic Operators -- 11 Spectral Asymptotics of Hypoelliptic Operators with Multiple Characteristics -- A Brief Review of the Bibligraphy -- Index of Notation.