Elementary Theory of Matrices by Paul Halmos is almost a concise and straightforward version of his famous book Finite-Dimensional Vector Spaces. Paul Halmos, known not only for his fundamental advances in various areas of mathematics but also for his exceptional expository skills, presents this short book to teach key topics. These include vector spaces and inner product spaces, linear transformations, spectral theory, dual spaces and tensor products, canonical forms, and limits of linear transformations.