Analyticity properties of scattering amplitudes: A review of some recent developments.- Recent development in hyperfunction theory and its application to physics (microlocal analysis of s-matrices and related quantities).- Micro-local calculus.- Microlocal study of S-matrix singularity structure.- Convolutors for ultrahyperfunctions.- Mass singularities of Feynman amplitudes.- Large momentum behaviour of Feynman amplitudes.- Spectral dependence of the analyticity domain of local vertex functions.- Asymptotics and light-cone singularities in quantum field theory.- Structure of singularities of Wightman-distributions and the Wilson-Zimmermann-expansion respectively lightcone-expansion.- Conformal invariance in Minkowskian quantum field theory and global operator expansions.- On some massless superrenormalizàble and nonrenormalizable theories.- The locality condition in parafermi field theory.- Bound state nature and deep inelastic structure functions.- The physical content of the statistical bootstrap and high energy hadron interaction.- Field theoretical approach to composite particle reactions.- Particles and bound states and progress toward unitarity and scaling.- Field theory of relativistic strings.- Results and problems in irreversible statistical mechanics of open systems.- The Wightman axioms and the mass gap for weakly coupled (?4)3 quantum field theories.- Soluble models and the meaning of nonrenormalizability.- Bound states and asymptotic fields in model field theories.- Feynman propagators associated with the Veneziano model.- Dual string models and quantum gravity.- Physical states satisfying supergauge conditions in dual resonance models.- The canonical quantization of a relativistic string.- Algebraic methods and quark structure.- Unitarity and asymptoticcondition in a model with dipole ghost.- Invariant gauge families inherent in Abelian-gauge field theory.- Space-time approach to anomalies in the Ward-Takahashi identities and implications in physical processes.- Dispersion approach to Ward-Takahashi identities.- Renormalization of supersymmetric gauge theories.- Stochastic calculus.- Asymptotic properties of the spectral distributions of disordered systems.- A remark to Harris's theorem on percolation.- The ergodicity of the motion of a particle in a potential field.- Ergodicity of some simple model systems of infinitely many particles.- New exact solutions of the classical Yang-Mills field equation.- Topology of Higgs fields.- Spontaneous breaking of chiral symmetry in a vector-gluon model.- Quantum field-theoretical approach to spontaneously broken gauge invariance.- Reviews on axiomatic study of symmetry breaking.- Structure of renormalized Feynman amplitudes.- On the regularization in the Callan-Symanzik equation.- The statistics of particles in local quantum theories.- Relaxation and fluctuation of macrovariables.- Holomorphic functions with a nonnegative imaginary part in the future tube.- Algebraic aspects of Wightman quantum field theory.- The infrared problem and non-fock representations of the canonical commutation relations.- Dynamical theories of Brownian motion.- Continuous representations of the test function algebra and the existence problem for quantum fields.- Unbounded derivations of C* algebras.- A method for making relativistic non-quantum systems by constructing the Hamiltonian and the other nine generating functions.- An algebraic approach to the theory of K-flows and K-entropy.- Symmetry restoration at finite temperature.- Critical behaviour of stationary random fields.- Phase transitions of continuous order.- Order of the phase transition related to the degeneracy and interaction with proposal for an exact problem.- The Heisenberg model on the Cayley tree.- Generalized Gell-Mann and low group Transformations: Scaling variables and cross-over effects.- Generalizations and applications of Callan-Symanzik equations to statistical mechanics in critical phenomena.- On the rigorous definition of superfluidity and superconductivity.- Variational problems and free boundary problems.- Uniqueness, analyticity and decay properties of correlations in equilibrium systems.- On the propagation of support of solutions to general systems of partial differential equations.- Wave propagation in a non-linear lattice.- Quantization of non-linear waves.- On the nonlinear diffusion equation of Kolmogorov-Petrovskii-Piskunov type.- Global solutions to the Broadwell's model of Boltzmann equation for a simple discrete velocity gas.- Scaling method for asymptotic evaluation in nonequilibrium statistical mechanics.- Self-entrainment of a population of coupled non-linear oscillators.- Thermodynamic limit of non-equilibrium systems.- Equilibrium states and ergodic properties of infinite systems.- Variational principles for Markov processes and Onsager principle.- Functional averages in statistical physics.- On the validity of collective variable description of bose systems.- Equilibrium statistical mechanics of one-dimensional classical lattice systems.- A look at the development of spectral and scattering theory in Japan.- On the Born-Oppenheimer approximation.- Abstract approaches to spectral and scattering theory, contributions from Japan.- Eigenfunction expansions for differential operators with operator-valued coefficients and their applications to the Schrödinger operators withlong-range potentials.- Asymptotic completeness in three-particle quantum mechanical scattering.- Decay and asymptotics for wave equations with dissipative term.- Treatment of three body problems in coordinate space.- Links between decay properties of correlations and analyticity of the pressure and correlation functions.- Linear response , stability , cluster properties.- Equilibrium and metastable states of classical systems.- Dynamical theories of Brownian motion.- Distribution of zeros and the equation of state.- New theorems on algebraic equation and its application to statistical physics.- Operator-valued-measure approach to spectra of two-dimensional classical harmonic lattices.- Models for relativistic statistical mechanics.- Path integrals in Riemannian manifolds.- Bose quantum field theory as an Ising ferromagnet: Recent developments.