These proceedings of the workshop on quantum probability held in Heidelberg, September 26-30, 1988 contains a representative selection of research articles on quantum stochastic processes, quantum stochastic calculus, quantum noise, geometry, quantum probability, quantum central limit theorems and quantum statistical mechanics.

Quantum Langevin equation in the weak coupling limit.- On the low density limit of Boson models.- Quantum stochastic flows and non abelian cohomology.- Quantum diffusions on involutive algebras.- Some Markov semigroups in quantum probability.- A quantum stochastic calculus in fock space of input and output nondemolition processes.- Stochastic transitions on preduals of von Neumann algebras.- Quantum stochastic calculus and a boson Levy theorem.- Locally independent boson systems.- Time-inhomogeneous and nonlinear quantum evolutions.- Quantum poisson processes: Physical motivations and applications.- Quantum central limit and coarse graining.- An open problem in quantum shot noise.- A method of operator estimation and a strong law of large numbers in von Neumann algkbras.- An analog of the Ito decomposition for multiplicative processes with values in a Lie group.- Stochastic dilations of quantum dynamical semigroups using one-dimensional quantum stochastic calculus.- Sluggish decay of preparation effects in low temperature quantum systems.- Almost sure convergence of iterates of contractions in noncommutative L2-spaces.- Duality transform as *-algebraic isomorphism.- Rigidity of the poisson convolution.- A discrete entropic uncertainty relation.- Working with Quantum Markov States and their classical analogues.- Dynamical entropy, quantum K-systems and clustering.- A continuous time version of Stinespring's theorem on completely positive maps.- The topology of the convergence in probability in a W*-algebra is normal.- First steps towards a Donsker and Varadhan theory in operator algebras.- Quantum conditional probability spaces.- Quantum diffusions on the rotation algebras and the quantum hall effect.- Quantum dirichlet forms, differential calculus and semigroups.-Gaussian states on bialgebras.- Quantum macrostatistics and irreversible thermodynamics.- Correction to the hydrodynamical approximation for groups of Bogoljubov transformations.- Bell's inequalities and quantum field theory.