Lattice instantons: What they are and why they are important -- Gauge fields on the lattice -- Lattice gauge theories -- Some frontiers in constructive quantum field theory and equilibrium statistical mechanics -- New proofs of long range order -- Number of phases in one component ferromagnets -- A survey of local cohomology -- Operator algebras and statistical mechanics -- Foundations of equilibrium quantum statistical mechanics -- Unbounded derivations of C*-algebras and corresponding dynamics -- to the flow of weights on factors of type III -- The von Neumann algebra of a foliation -- Nuclearity and the C*-algebraic flip -- On the Connes spectrum of simple C*-dynamical systems -- Quantum field theory of massless particles and scattering theory -- Scattering theory in quantum mechanics and asymptotic completeness -- Static solitons in more than one dimension -- Geometry of Yang-Mills fields -- Periodic solitons and algebraic geometry -- Yang--Mills equations as inverse scattering problem -- Nonlinear evolution equations solvable by the inverse spectral transform -- Quantization of particle-like solutions in field theory -- Topics in infinite dimensional analysis -- Mathematical foundations of the renormalization group method in statistical physics -- On the renormilization group for the hierarchical model -- Fluctuationes in Curie-Weiss exemplis -- On the problem of the mathematical foundation of the Gibbs postulate ie classical statistical mechanics -- Dynamical systems with turbulent behavior -- Generic properties of Navier-Stokes equations -- A limit theorem for turbulent diffusion -- Many particle scattering aitlitudes -- A Remark on equations of motion in asymptotically free theories -- Short-distance expansion for products of current-like operators -- The use of exterior forms in field theory -- On extensions of flows in the presence of sets of singularities -- On the uniqueness of the equilibrium state for plane rotators -- A geometric approach to the solution of conformal invariant field equations -- Stability, detailed balance and KMS condition for quantum systems -- Stochasticity and irreversibility in infinite mechanical systems -- Why the KMS states? -- A comment to the talk by E. Seiler.