Computational engineering is the treatment of engineering tasks with computers. It is based on computational mathematics, which is presented here in a comprehensive handbook. From the existing rich repertoire of mathematical theories and methods, the fundamentals of engineering computation are here presented in a coherent fashion. They are brought into a suitable order for specific engineering purposes, and their significance for typical applications shown. The relevant definitions, notations and theories are presented in a durable form which is independent of the fast development of information and communication technology.