This book reviews a range of standard mathematical tools used to solve optimization problems. It discusses the conditions under which function optima exist, considering both single-variable and multi-variable functions. Because resources are often limited, special attention is given to constrained optimization problems, where the domain of the function is restricted. Convex and linear programming problems are examined in greater detail due to their favorable numerical properties. Finally, the book addresses a number of concepts related to optimization problems involving multiple agents or multiple objectives. The main text is accessible to students of economics as well as to those pursuing more technically oriented fields of study. Its aim is to provide students with a clear understanding of the underlying concepts, an intuitive grasp of the conditions under which specific mathematical tools can be applied, and practical guidance on their use. Mathematical details required for full theoretical rigor are largely omitted from the main text, but additional rigor is provided through supplementary exercises.