Optimization is a foundational topic in mathematics, underpinning nearly all of our modern industrial and technological world. Assuming only basic knowledge of linear algebra and calculus, this book provides a rapid, yet thorough, overview of applied mathematical optimization for advanced undergraduates, beginning graduate students, or practitioners in engineering and science. The text opens with an 'Optimization Bootcamp', introducing methods at a beginning level, before progressing to deep-dives into advanced topics and research-ready methods. The focus throughout is on modern applications of machine learning, inverse problems, and control. Rich pedagogy includes Python code with simple working examples and advanced case studies. Every section is accompanied by YouTube lectures to encourage interaction with the material. Using intuitive explanations, this book makes the material as simple and interesting as possible, while still having the depth, breadth and precision required to empower use in research and real-world applications.