The course aims to provide an overview of convex and non-convex optimization including duality, KKT conditions, high performance algorithms and recent developments in linear and nonlinear optimization. The course is divided into 3 chapters. Chapter 1 introduces mathematical programming and some practical applications and models. Chapter 2 focuses on theoretical knowledge including dual problem, duality theorems, and optimal conditions. Chapter 3 presents algorithms solving unconstrained and constrained optimization problems.