This chapter covers several topics of Linear Algebra, some of them not always treated in standard courses of mathematics for economic and financial analysis. Section 1.1 presents the axioms characterizing a linear space (or vector space) over a real field. Section 1.2 is concerned with basic notions on vectors in \(\mathbb {R}^{n}\) and with basic notions on topology for n -dimensional Euclidean spaces. Section 1.3 discusses basic topics on matrices, determinants and linear equations systems. Section 1.4 is concerned with linear functions or linear maps from \(\mathbb {R}^{n}\) to \( \mathbb {R}^{m}.\) Section 1.5 gives the basic notions on complex numbers, which are an essential tool to introduce the next section. Section 1.6 discusses eigenvalues and eigenvectors of square matrices: this subject is important in several areas of applied mathematics, such as the theory of quadratic forms (next section), the theory of nonnegative square matrices (Perron-Frobenius theorems), the analysis of several linear economic models of equilibrium and growth (Sect. 1.9), continuous and discrete dynamical systems (Chaps. 6 and 7 ). Quadratic forms (unconstrained and constrained), Perron-Frobenius theorems, an introduction to a simple Leontief input-output model and an introduction to a particular Sraffa economic model are the subjects of Sects. 1.7, 1.8, and 1.9.