This book is a translation and revision of an earlier textbook in Swedish by the first two authors. It is intended as a textbook for an introductory course in scientific computation at an advanced undergraduate level. In a modern programming environment such as MATLAB it is possible by means of simple commands to perform advanced calculations on a personal computer. In order to use such a powerful tool efficiently it is necessary to have a good knowledge of numerical methods and algorithms and to know about their properties. The book describes and analyses numerical methods for error analysis, differentiation, integration, interpolation and approximation, and the solution of non-linear equations, linear systems of algebraic equations and systems of ordinary differential equations. Principles and algorithms are illustrated by examples in MATLAB. At the end of each chapter questions on theory and computer exercises are given. Some of the MATLAB codes and supplementary material are available from the books web page.