Algorithms play an increasingly important role in almost all areas of mathematics. This textbook is suitable for beginners and complements the traditional lectures on analysis and linear algebra with a third foundational mathematics course, which the authors have taught multiple times at the University of Bonn in recent years. The aim of this book is to impart fundamental mathematical skills, particularly regarding the design and analysis of algorithms as well as their implementation. In addition to some fundamental algorithms (e.g., the Sieve of Eratosthenes, Euclidean algorithm, sorting algorithms, graph algorithms, Gaussian elimination), it also covers basic data structures, graph theory fundamentals, and numerical issues. Furthermore, basic programming skills are taught, and it demonstrates how to implement algorithms in C++.