The goal of this thesis is to use Python in order to estimate the eigenvalues of regular Sturm-Liouville problems with Dirichlet boundary conditions. We will study the Sturm-Liouville problem and the properties of the eigenvalues and eigenfunctions. Moreover, we will discuss and use the Prufer transformation and a Prufer-based shooting method to implement the Python code. Finally, we will test the code by computing the first ten eigenvalues of different examples.