This book offers a historically oriented introduction to algorithmics, the study of algorithms, in mathematics, computer science, and beyond. Key features and objectives include: elementary and illustrative content, consideration of historical development, motivation of terms and methods through concrete, meaningful examples, incorporating modern tools. As supplementary media, computer- and internet-specific interaction and visualization options are provided free of charge. The work is aimed at students and educators in schools and universities, as well as non-specialists interested in the topics of "computers/algorithms/programming," including their historical and humanities dimensions.