This is a set of notes written as part of teaching, graduate course on the finite element method, in the Department of Aeronautical Engineering. This book covers the basics and application of Finite Element Method in Structural, Fluid flow and Heat Transfer problems. Finite Element Analysis was developed as a numerical method of stress analysis, but now it has been extended as a general method of solution to many complex engineering and physical science problems. As it involves a lot of calculations, its growth is closely linked with the developments in computer technology.