Transport phenomena problems that occur in engineering and physics are often multi-dimensional and multi-phase in character. When using numerical methods, the spectral method is particularly useful and efficient. This book is designed primarily to train students and non-specialists in the application of the spectral method for solving problems that model fluid flow in closed geometries with heat or mass transfer. To benefit from this book, the reader should have a working knowledge of fluid mechanics and heat transfer and should be familiar with basic concepts of linear algebra, including spectral decomposition of matrices and solvability conditions for inhomogeneous problems. The book is not intended to provide a ready-to-use program that is all-purpose, nor does it cover all mathematical proofs. The focus of this tutorial is on the use of spectral methods for spatial discretization.