This book is a comprehensive guide to the theory, methods, and applications of mathematical optimization using Python to solve real-world business problems. It begins with a practical introduction to Python, covering data types, objects, functions, and methods. This foundation is followed by key statistical concepts, including probability, inference, and hypothesis testing. The book then explores numerical simulation techniques, setting the stage for the core topics of continuous and discrete optimization. Readers will gain a deep understanding of classical optimization algorithms and how to implement them in Python. Designed for students, professionals, and researchers alike, this book combines theoretical rigor with hands-on coding examples and real-world case studies to equip readers with the skills needed for solving complex optimization challenges in modern data-driven environments.