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Optimization formulations and algorithms have long played a central role in data analysis and machine learning. In the era of big data, the need to solve large-scale optimization problems is ubiquitous in essentially all quantitative areas of human endeavor, including industry and science. This course is a mathematically rigorous and comprehensive introduction to the field of large-scale optimization for data science and machine learning, and is based on the latest results and insights. We discuss the most important algorithms in the area, with analysis of their convergence and complexity properties, as well as their practical implementations. Applications of the methods covered in the course can be found virtually in all fields of data science including text analysis, page ranking, speech recognition, image classification, finance and decision sciences. Prerequisites: background in Linear Algebra (or Computational Linear Algebra), Multivariable Calculus, Probability, and a basic knowledge of programming - experience with at least one high-level computing language (e.g.: Python, Matlab, Julia, C, ….).