This is a textbook written for mechanical engineering students at the first year graduate level. As such, it emphasizes the development of finite element methods used in applied mechanics. The book starts with fundamental formulations of heat conduction and linear elasticity and derives the weak form (i.e. the principle of virtual work in elasticity) from a boundary value problem that represents the mechanical behaviour of solids and fluids. Finite element approximations are then derived from this weak form. The book contains many useful exercises and the author appropriately provides the student with computer programs in both BASIC and FORTRAN for solving them. Furthermore, a workbook is available with additional computer listings, and also an accompanying disc that contains the BASIC programs for use on IBM-PC microcomputers and their compatibles. Thus the usefulness and versatility of this text is enhanced by the student's ability to practise problem solving on accessible microcomputers.