Knowledge in the areas of Data Science and Machine Learning is increasingly expected from mathematics graduates and consequently, students of mathematics ask for these subjects to be included in the standard curricula. The idea behind this textbook is to present canonical Data Science and Machine Learning topics in a form tailored to the target audience of mathematics students. In doing so, our number one priority is a rigorous treatment that fosters profound understanding of the methods discussed. This includes in particular to always work out why exactly a method succeeds and to outline its limitations. This textbook is intended for students of mathematics who have completed the foundational courses of their undergraduate studies and now want to specialize in Data Science and Machine Learning. It introduces the reader to the most important topics in the latter areas focusing on rigorous proofs and a systematic understanding of the underlying ideas. The textbook comes with 121 classroom-tested exercises. Topics covered include k-nearest neighbors, linear and logistic regression, clustering, best-fit subspaces, principal component analysis, dimensionality reduction, collaborative filtering, perceptron, support vector machines, the kernel method, gradient descent and neural networks.