Partial Integro-Differential Equations, Coagulation-Fragmenation Models: Well-posedness, Regularity, Mass-conservation, Gelation, Large time behaviour, Stationary solutions, Self-similar profiles, Numerical Methods, Error Analysis, Stochastic Partial Differential Equations: Well-posedness, Regularity and Convergence Analysis of Numerical Methods, Regularization Theory for Inverse Problems: Variational Regularization and Iterative regularization, Stability Estimates, Regularized Solutions, Convergence, Convergence Rates