This textbook offers a comprehensive and accessible introduction to machine learning with the Julia programming language. It bridges mathematical theory and real-world practice, guiding readers through both foundational concepts and advanced algorithms. Covering topics from essential principles like Kullback-Leibler divergence and eigen-analysis to cutting-edge techniques such as deep transfer learning and differential privacy, each chapter delivers clear explanations and detailed algorithmic treatments. Sample code accompanies every major topic, enabling hands-on learning and faster implementation. By leveraging Julia's powerful machine learning ecosystem -- including libraries such as Flux.jl, MLJ.jl, and more -- this book empowers readers to build robust, state-of-the-art machine learning models. Ideal for students, researchers, and professionals alike, this textbook is designed for those seeking a solid theoretical foundation in machine learning, along with deep algorithmic insight and practical problem-solving inspiration.