Mathematical pictures at a data science exhibition In the past few decades heuristic methods adopted by big tech companies have complemented existing scientific disciplines to form the new field of Data Science. This text provides deep and comprehensive coverage of the mathematical theory supporting the field. Composed of 27 lecture length chapters with exercises it embarks the readers on an engaging itinerary through key subjects in data science including machine learning optimal recovery compressive sensing (also known as compressed sensing) optimization and neural networks. While standard material is covered the book also includes distinctive presentations of topics such as reproducing kernel Hilbert spaces spectral clustering optimal recovery compressive sensing group testing and applications of semidefinite programming. Students and data scientists with less mathematical background will appreciate the appendices that supply more details on some of the abstract concepts