In this study a Computational Fluid Dynamics (CFD) code to solve the two-dimensional subsonic flow around simple geometry airfoils is developed. The presented method departs from the Euler equations and through a finite-volume explicit time-marching method produces the solution of all the variables of the potential flow. Furthermore, some variations of the main code using different discretization schemes are used in order to compare their results. Also a simple meshing code was also designed and included in the main software in order to produce the structured grid the solver works with. The fundamentals of all of them are also presented in this study along with a detailed explanation of the software's functioning and a proper validation of the results. Finally, further code improvements are suggested