The purpose of this chapter is to review important fundamental concepts in linear algebra, as a foundation for the remaining portion of this text. We first discuss the foundational elements of linear algebra upon which the rigor of linear algebra rests, such as linear independence, linear vector spaces, subspaces, range, nullspace and related ideas, rank, bases, etc. and matrix multiplication from a “big block” perspective. We then discuss vector norms and close the chapter with a discussion on determinants. The theory in the following chapters depends on the reader having a solid grasp of the concepts presented in this chapter.