In this chapter, we explore the determinants of square matrices, a fundamental quantity in linear algebra and a critical tool for computations in Feynman integrals. Starting with permutations and antisymmetrization, our focus is on the structure and properties of determinants, providing a detailed examination of Laplace expansion and the Cauchy-Binet formula. Additionally, we introduce the determinant of linear maps, emphasizing its role in broader algebraic frameworks. These tools are essential for classical linear algebra and modern applications in theoretical physics.