Computational methods are an integral part of most scientific disciplines, and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms with the aim of familiarizing the reader with the field?s theoretical foundations and providing the practical skills to use and develop computational methods. Methods in Computational Science extends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing, ? is centered around a set of fundamental algorithms presented in the form of pseudocode, ? presents theoretical material alongside several examples and exercises, and ? provides Python implementations of many key algorithms. Methods in Computational Science is a textbook for computer science and data science students at the advanced undergraduate and graduate level. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. Because the text is self-contained, it can also be used to support continuous learning for practicing mathematicians, data scientists, computer scientists, and engineers in the field of computational science.