This book expresses the diversity of optimization and approximation along with their broad context through tasks, their solutions, and useful applications. The focus is on utilizing methods of applied analysis to recognize the structure and properties of the problems and to derive manageable optimality conditions that facilitate and simplify the treatment of the tasks. Many practical problem statements lead to convex or non-convex optimization problems, multi-criteria optimization problems, location problems, issues in risk theory, actuarial mathematics, optimization problems with uncertainties, and models from signal theory, which are discussed in the tasks presented. References to online available software are provided. The book is aimed at students and educators in mathematics.