Background on Algebraic Structures. Overview of Algebraic Systems. Permutations. Polynomials. Matrices. Basic Matrix Operations. Determinants via Calculations. Concrete vs. Abstract Linear Algebra. Matrices with Special Structure. Hermitian, Positive Definite, Unitary, and Normal Matrices. Jordan Canonical Forms. Matrix Factorizations. Iterative Algorithms in Numerical Linear Algebra. The Interplay of Geometry and Linear Algebra. Affine Geometry and Convexity. Ruler and Compass Constructions. Dual Spaces and Bilinear Forms. Metric Spaces and Hilbert Spaces. Modules, Independence, and Classification Theorems. Finitely Generated Commutative Groups. Axiomatic Approach to Independence, Bases, and Dimension. Elements of Module Theory. Principal Ideal Domains, Modules over PID’s, and Canonical Forms. Universal Mapping Properties and Multilinear Algebra. Introduction to Universal Mapping Properties. Universal Mapping Problems in Multilinear Algebra. Appendix: Basic Definitions. Sets. Functions. Relations. Partially Ordered Sets. Further Reading. Bibliography. Index.