This is an intermediate linear algebra course aimed at a diverse group of students, including sophomores in applied and computational mathematics, computer science, and information and data sciences, as well as graduate students in science and engineering. The main goal of the course is to provide an introduction to the fundamental ideas, concepts, and methods of applied linear algebra and illustrate them with important applications. Topics covered include linear systems, vector spaces and bases, fundamental matrix subspaces, inner products, norms, k-means algorithm, positive-definite and Gram matrices, application to text classification, least squares solutions and applications to data fitting, orthogonality, the QR factorization, eigenvalues and eigenvectors, the Gerschgorin theorem, the Perron-Frobenius theorem, the PageRank algorithm, the spectral theorem, optimization principles for eigenvalues, principal component analysis, spectral method for graph partitioning, and singular value decomposition with its applications.