This book covers the numerical solution of elliptical partial differential equations, an important applications of finite elements, and addresses aspects such as saddle problems, which require a more in-depth mathematical treatment. A chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering. This text is for graduate students who do not have background in differential equations, but require an introduction to finite element methods. The book was first published in German as Finite Elemente by Springer Verlag, 1992. This second English edition (the first English edition was published in 1996) is updated and includes new material on Fortin interpolation and the multigrid theory.