This document outlines the syllabus for the “Numerical Linear Algebra” course (CITHN2006), a 18-lecture course focused on applying numerical linear algebra techniques to computational science and information engineering. The course covers foundational linear algebra concepts, introduces the Julia language with coding assignments, and progresses through various methods for solving linear systems, eigenvalue problems, and matrix function evaluations – including direct methods, iterative techniques, and randomized algorithms. Each lecture includes theoretical presentations and associated homework/coding assignments, providing a hands-on approach to learning.