This text presents an introduction to the application of the finite ele ment method to the analysis of heat transfer problems. The discussion has been limited to diffusion and convection type of heat transfer in solids and fluids. The main motivation of writing this book stems from two facts. Most introductory texts attempt to teach FEM from a struc tural engineering background, which may distract non-structural engineers from pursuing this important subject with full enthusiasm. As mentioned earlier this book may be used to learn FEM by beginners, this may include undergraduate students and practicing engineers. However, there is enough advanced material to interest more experienced practitioners.