This volume investigates the evolution of probability theory from its classical roots to modern applications through a collection of advanced graduate-level courses. The book compiles lecture notes from six distinct courses delivered at a CIMPA Summer School, covering topics such as the asymptotic behavior of heat kernels in unbounded domains, spin systems with long-range interactions, non-linear Dirichlet problems and integration, first-passage percolation, the central limit theorem for Markov processes, and stochastic orders and stopping times in Brownian motion. While designed for graduate students, the specialized material is also intended to engage experts in the field.

The collection of advanced courses presented in this volume offers a specialized look into various facets of modern probability theory. The material is structured for graduate students, suggesting a rigorous and in-depth exploration of each topic. The inclusion of topics like spin systems and non-linear integration points to a focus on interdisciplinary connections with mathematical physics and analysis. The breadth of subjects covered indicates a comprehensive approach to advanced probability, catering to those with a strong foundational understanding.