Data-driven discovery is revolutionizing the modeling, prediction, and control of complex systems. Aimed at advanced undergraduate and beginning graduate students, this textbook provides an integrated viewpoint that shows how to apply emerging methods from data science, data mining, and machine learning to engineering and the physical sciences. Data-driven discovery is revolutionizing the modeling, prediction, and control of complex systems. This textbook brings together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science. It highlights many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. Aimed at advanced undergraduate and beginning graduate students in the engineering and physical sciences, the text presents a range of topics and methods from introductory to state of the art.