Proceedings of the Summer Conference on Algebras and Mathematical Physics in honor of the 60th birthdays of Profs. H.J. Borchers, N.M. Hugenholtz, R.V. Kadison, and D. Kastler.

Includes bibliographies.

A biographical sketch of HansJurgen Borchers ; A biographical sketch of N. M. Hugenholtz ; A biographical sketch of Richard V. Kadison ; A biographical sketch of Daniel Kastler ; Bogoliubov automorphisms and Fock representations of canonical anticommutation relations ; On the interplay between spectrum condition and locality in quantum field theory ; The structure of local algebras of observables ; How the ^\ast lgebraic formulation of statistical mechanics helps understanding the approach to equilibrium ; KMS structures in geometric quantization ; Perturbations and KMS states in ^\ast ynamical systems (generalization of the absence theorem of phase transition to continuous quantum systems) ; bf Z2 raded cyclic cohomology within the differential envelope ; YangMills for noncommutative twotori ; Nonstable heory and noncommutative tori ; Nonlinear states on ^\ast lgebras ; Cones of positive maps ; On the geometry of positive maps in matrix algebras ; Differential operators on ^\ast lgebras ; Derivations and free group actions ; Automatic continuity of derivations on eigenspaces ; Dynamics in continuous quantum systems ; Kuiper's theorem for Hilbert modules ; Feynman's operational calculus, generalized Dyson series and the Feynman integral ; An index theory for continuous semigroups of ast ndomorphisms of mathfrak B(\mathfrak H) and rm II_1 factors ; Multivariable Toeplitz operators, Jordan algebras and index theory ; On multilinear completely bounded module maps ; On the classification of noncommutative tori. III ; The joint modular structure of an inclusion of von Neumann algebras ; Central sequences in crossed products Klaus Fredenhagen ; Marinus Winnink ; Erling Strmer ; Rudolf Haag ; Huzihiro Araki ; HJ Borchers ; K Fredenhagen ; N M Hugenholtz ; Gerard G Emch ; Shoichiro Sakai ; Daniel Kastler ; Alain Connes and Marc A Rieffel ; Marc A Rieffel ; William Arveson ; Erling Strmer ; Jun Tomiyama ; Derek W Robinson ; Ola Bratteli ; Ola Bratteli and Akitaka Kishimoto ; Shoichiro Sakai ; Joachim Cuntz and Nigel Higson ; Gerald W Johnson and Michel L Lapidus ; Robert T Powers ; Harald Upmeier ; Edward G Effros ; Berndt Brenken Joachim Cuntz George A Elliott and Ryszard Nest ; Roberto Longo ; Richard H Herman and Vaughan F R Jones