Maxima is a computer algebra system (CAS) like Maple and Mathematica. Thus it is a powerful tool for the manipulation of symbolic and numerical expressions, including di↵erentiation, integration, vectors, matrices etc. Maxima was developed from 1968−1982 at MIT (Massachusetts Institute of Technology) as the first comprehensive computer algebra system allowing not only for numerical, but also symbolical computation. It is employed in education and research by mathematicians, physicists, engineers, and economists, coping with the major commercial CAS systems of today. It also provides commands for plotting functions, curves and data in two and three dimensions. In opposition to other CAS Maxima has a quite long history and is open source software.
First chapter is devoted for introducing Maxima software. We also discuss how to load packages for executing various commands. Furthermore, we study basic Algebra. In second chapter, we demonstrate to draw 2D and 3D plots for various functions. In third chapter, we study Discrete Mathematics, specially we focus on logic, boolean algebra, counting and recurrence relation. Chapter four is devoted for calculus and in the last chapter, we study Matrix Algebra.