A model for crystallization: A variation on the Hubbard model -- First order phase transitions and perturbation theory -- Low temperature continuous spin Gibbs States on a lattice and the interfaces between them - a Pirogov Sinai type approach -- Spin glasses, effective decrease of long-range interactions -- Analyticity in some models of quantum statistical mechanics -- K-theory of C*-Algebras in solid state physics -- Quantum field theory without cutoffs- renormalizable and nonrenormalizable -- Renormalization group methods in rigorous quantum field theory -- Renormalisation group methods for circle mappings -- Correlations and fluctuations in charged fluids -- Models of statistical mechanics in one dimension originating from quantum ground states -- Why do bosons condense? -- Black holes and quantum mechanics -- Quantum field theory and gravitation -- A remark on antiparticles -- Notes on the canonical anticommutation relations -- A differential - geometric setting for BRS transformations and anomalies -- Renormalization of a hierarchical fermion model in two dimensions -- Gribov copies and absence of spontaneous symmetry breaking in compact U(1) lattice higgs models -- Renormalization group approach for the Ising model as an approximate solution of the diaphantian system of equations -- Transformation of the transfer matrix for the Ising model under decimation -- Some results concerning the localization problem in one-dimensional quasiperiodic systems -- Random walks on random lattices -- The role of transverse fluctuations in multidimensional tunneling -- Self-similar temporal behavior of random walks in random media -- Loop expansions in the presence of Gribov copies -- Non-existence of long-range-order for a certain 1D model and the soliton picture -- Quantum fields out of thermal equilibrium -- Statistical mechanical approach to the construction of four dimensional boson field theories -- Correlation lengths at zero temperature in one dimension -- Horizontal Wilson loops in finite temperature lattice gauge theories -- The random bond Potts and Ashkin-Teller models -- Spectral line shapes in quantum Markov scattering -- Exact bogoliubov limits for the Bassichis-Foldy model and continued fractions.