The book 'Probability and Partial Differential Equations in Modern Applied Mathematics' explores the role of probabilistic methods in modern applied mathematics. It highlights both the application of these methods as analytical tools and their significance in modeling. Within the research community of applied mathematics, there is an increasing recognition that stochastic methods play a central role in the formulation and analysis of various problems in the sciences and engineering. By using probabilistic representations of solutions to partial differential equations, which appear as deterministic models, the possibilities of stochastic analysis and probabilistic limit theory can be leveraged. This opens up new perspectives for modeling complex systems and leads to interesting mathematical questions at the intersection of probability, dynamical systems, numerical analysis, and partial differential equations. The book is aimed at researchers and students interested in probabilistic methods and their applications in the natural sciences and engineering.