This chapter introduces basic methods for solving a linear system of equations. Gauss elimination is the most fundamental method; however, it is not appropriate for all problems. Iterative methods, such as Gauss-Jacobi and Gauss-Seidel, are introduced as well. Stability and convergence concepts are an important part of these iterative methods. If more information (data points) for a problem is given than is needed for a solution, this leads to an overdetermined system of equations. Many solutions are possible; an optimal solution, called least squares, is described here. Three case studies motivate the ideas in this chapter.