Mathematical data science is a field that combines mathematical techniques with data science methods to extract insights and knowledge from data. It involves working with data at all stages of the data lifecycle, from collection and storage to cleansing and processing, the analysis and visualization of data, and the communication of the results and findings. Data scientists use a variety of tools and techniques to analyze data, including mathematical concepts and models, artificial intelligence techniques, machine learning algorithms, statistical analysis, and data visualization. Furthermore, data science can be used to make predictions, identify patterns, and draw conclusions from data, and it is applied in a variety of areas, including business, industry, and medicine. It is a rapidly evolving field, and data scientists are expected to stay up to date with new tools, techniques, and technologies. This Reprint is a collection of articles on a wide range of topics in the field of mathematical data science, with applications in business, industry, and medicine. The proposed methods and concepts are discussed in detail and illustrated with several real-life data examples.