This textbook was initially developed for the introductory course in finite element methods at the Department of Mechanical Engineering and Applied Mechanics, the University of Michigan, Ann Arbor, Michigan. It is based on four years of teaching experience of first-year graduate students and some senior undergraduate students in the engineering college. Because of the mechanical engineering environment, heat conduction problems are covered, as are standard stress analysis of solids and structures. Many small-size BASIC and FORTRAN programs are given so that readers can apply them to solve exercises using either microcomputers such as IBM PCs and compatibles or mainframes of computer networks that support FORTRAN iv. BASIC programs are available in separate volumes with a diskette for the IBM PC and compatibles by reader's request (see back of book for ordering instructions). FORTRAN programs are also available to readers who specially request them from the author. At present, BASIC compilers are available for some microcomputers in order to improve speed of computation. In the author's opinion, they are very impressive and encourage the use of microcomputers even for finite element methods. It is noted, however, that these programs are primarily designed for educational purposes – to teach the theory of finite element methods.