Maximise student engagement and understanding of matrix methods in data-driven applications with this modern teaching package. Students are introduced to matrices in two preliminary chapters, before progressing to advanced topics such as the nuclear norm, proximal operators and convex optimization. Highlighted applications include low-rank approximation, matrix completion, subspace learning, logistic regression for binary classification, robust PCA, dimensionality reduction and Procrustes problems. Extensively classroom-tested, the book includes over 200 multiple-choice questions suitable for in-class interactive learning or quizzes, as well as homework exercises (with solutions available for instructors). It encourages active learning with engaging 'explore' questions, with answers at the back of each chapter, and Julia code examples to demonstrate how the mathematics is actually used in practice. A suite of computational notebooks offers a hands-on learning experience for students. This is a perfect textbook for upper-level undergraduates and first-year graduate students who have taken a prior course in linear algebra basics.