Lefschetz Distribution of Lie Foliations -- Torsion, as a Function on the Space of Representations -- The K-theory of Twisted Group Algebras -- Twisted Burnside Theorem for Two-step Torsion-free Nilpotent Groups -- Ihara Zeta Functions for Periodic Simple Graphs -- Adiabatic Limits and the Spectrum of the Laplacian on Foliated Manifolds -- On the Non-standard Podle? Spheres -- Boundaries, Eta Invariant and the Determinant Bundle -- Elliptic Theory on Manifolds with Corners: I. Dual Manifolds and Pseudodifferential Operators -- Elliptic Theory on Manifolds with Corners: II. Homotopy Classification and K-Homology -- Dixmier Traceability for General Pseudo-differential Operators -- Topological Invariants of Bifurcation -- Modified Hochschild and Periodic Cyclic Homology -- L 2-invariants and Rank Metric -- Group Bundle Duality, Invariants for Certain C*-algebras, and Twisted Equivariant K-theory -- A New Topology on the Space of Unbounded Selfadjoint Operators, K-theory and Spectral Flow.