This book is the main course literature in the course Computational Engineering, which comprises 22,5 ECTS (European Credit Transfer System), within the programme of Master of Science in Mechanical Engineering with emphasis on Structural Mechanics at Blekinge Institute of Technology. The book starts with rather simple numerical methods for ordinary differential equations and ends with advanced topics such as finite element procedures for systems of transient, non-linear and coupled partial differential equations. Several topics from physics and engineering are included to support the study of the numerical methods.