Many engineering problems (including numerous issues encountered by Master's and Ph.D. students in their theses) can ultimately be modeled as the minimization or maximization of a cost function under specific constraints. Various algorithms exist for performing this optimization, such as the steepest descent method, Newton's method, Quasi-Newton methods, and others. The primary goal of this course is to provide a comprehensive review of existing optimization algorithms and to familiarize students with the various methods and conditions for their application. This course will not be limited to convex constraints but will address the general case. However, there will be some discussion on convex problems and how certain theorems become simpler in that context. Conversely, specific methods for convex problems will also be covered. Therefore, this course may also be referred to as "Non-Convex Optimization," in contrast to another course focused solely on convex problems, which could be called "Convex Optimization."