"In the past few decades, the Finite Element Method (FEM) has been developed into a key indispensable technology in the modelling and simulation of various engineering systems. In the development of an advanced engineering system, engineers have to go through a very rigorous process of modelling, simulation,visualization,analysis, designing, prototyping, testing, and finally, fabrication/construction. As such, techniques related to modelling and simulation in a rapid and effective way play an increasingly important role in building advanced engineering systems, and therefore the application of the FEM has multiplied rapidly. This book provides unified and detailed course material on the finite element method that can be understood by both undergraduate, graduate and research students without the usual prerequisites required by most available texts in this area. The book is written primarily as a basic learning tool for the undergraduate students in civil and mechanical engineering, graduate and research students in graduate and Ph. D. levels whose main interest is in Magnetohydrodynamic fluid flow problems in presence of heat and mass transfer. The text is geared toward those who want to apply the finite element method to solve practical physical problems in MHD fluid flows. Note that the focus of this book is on developing a good understanding of the fundamentals and principles of linear finite element analysis. The author has chosen MATLAB as it can easily handle linear analyses, however, with further reading readers could also extend the use of MATLAB for projects involving non-linear finite element analyses too."