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Data science is about solving problems based on observations and data collected in the real world. Problems may range from the mundane to difficult scientific questions, for example, rating movies for recommendation systems, understanding the earning power of American taxpayers, increasing revenue for a business, spam, controlling the spread of misinformation through the internet, global warming, or the expansion of our universe. Our ability to generate, gather, and store volumes of data in the order of tera- and exo-bytes daily has far outpaced our ability to derive useful information from it in many fields, with available computational resources. The overarching goal of this book is to provide a practical and fairly complete, but not encyclopedic, review of Data Science (DS) through the lens of Dimensionality Reduction (DR). The intended audience consists of professionals and/or students in any domain science who need to solve problems to answer questions about their domain based on data. Domain science is a fairly vague term that refers to a specialized area of human knowledge characterized by specific questions about a certain aspect of reality (like what is motion in physics, what are physical objects made of in chemistry, what is life in biology, and so forth.) In addition to the well-established sciences, they include just about any area where data can be recorded and analyzed to answer questions concerning the population of individuals or objects the data is about. Data science presents a singular approach to problem solving when compared to more established sciences. Traditional sciences are motivated by understanding our world in order to survive and thrive. That requires a degree of analysis and theorizing to understand the specific phenomena involved and to enable predictive power. By contrast, with the advent of computer science and its abstractions into the information age (as embodied by the internet and web for example), tools have been created that can be used regardless of the specific domain. Once this threshold is crossed, then it is a natural next step from mathematics and statistics to synergistically combine them with the powerful computational tools developed by computer science to create a new science that is more than the sum of the parts, hence data science.