As mentioned above, this course will begin with a 2-part overview of fundamental iterative methods. Part I (2 hours) will cover topics such as Jacobi, Gauss-Seidel, SOR, matrix splittings, convergence properties, and acceleration schemes. Part II (2 hours) will introduce Krylov methods such as Conjugate Gradient, Lanczos, Arnoldi, and the Generalized Minimum Residual (GMRES) methods. Other topics presented include preconditioning, optimality, convergence properties, finite termination, and recurrence relations. The intent of this review is to re-introduce iterative methods and to prescribe classical references for outside reading. After the review, students will be better-prepared to study the relationships, properties, and applicability of the more recent Krylov methods proposed for the solution of nonsymmetric linear systems.