Continuous Path Processes.- Continuous-Path Random Processes: Mathematical Prerequisites.- Basic Concepts and Examples in Finance.- Hitting Times: A Mix of Mathematics and Finance.- Complements on Brownian Motion.- Complements on Continuous Path Processes.- A Special Family of Diffusions: Bessel Processes.- Jump Processes.- Default Risk: An Enlargement of Filtration Approach.- Poisson Processes and Ruin Theory.- General Processes: Mathematical Facts.-...