By mathematical modeling we describe the transformation of a concrete question or problem from the applied sciences (physics, chemistry, biology, engineering, economics, …) in a well-defined mathematical problem formulation. In this lecture we will get familiar with several modeling classes and their solution. Due to the complexity of systems in the applied sciences mostly a closed analytical solution of the model can not be determined such that a solution will be obtained based on computational simulation. We will introduce the simulation techniques and software packages for the corresponding model classes and will discuss actual concrete examples with a light focus on biological questions.