This study provides an introduction to computational fluid dynamics, focusing on the mathematical framework and numerical methods for solving fluid flow problems. The first part defines the properties and behavior of fluids, including the Navier-Stokes equations, which describe the evolution of fluid flow and properties. The second part discusses spatial and temporal discretization methods, such as finite differences and control volumes, to transform differential equations into numerical solutions. The third part applies these methods to two examples: convective-diffusive transport of a scalar property and fluid flow in a driven cavity. The study emphasizes the importance of incompressibility and homogeneity conditions for fluid dynamics problems and introduces the concept of dynamic similarities through the Reynolds number. Additionally, it covers the Helmholtz-Hodge decomposition, which is crucial for understanding the role of pressure in incompressible homogeneous viscous fluids. The research was conducted in collaboration with the Centre Tecnològic de Transferència de Calor (UPC) and supervised by Dr. Asensi Oliva.This study provides an introduction to computational fluid dynamics, focusing on the mathematical framework and numerical methods for solving fluid flow problems. The first part defines the properties and behavior of fluids, including the Navier-Stokes equations, which describe the evolution of fluid flow and properties. The second part discusses spatial and temporal discretization methods, such as finite differences and control volumes, to transform differential equations into numerical solutions. The third part applies these methods to two examples: convective-diffusive transport of a scalar property and fluid flow in a driven cavity. The study emphasizes the importance of incompressibility and homogeneity conditions for fluid dynamics problems and introduces the concept of dynamic similarities through the Reynolds number. Additionally, it covers the Helmholtz-Hodge decomposition, which is crucial for understanding the role of pressure in incompressible homogeneous viscous fluids. The research was conducted in collaboration with the Centre Tecnològic de Transferència de Calor (UPC) and supervised by Dr. Asensi Oliva.