This chapter introduces basic algebraic structures and concepts used in the rest of the book. We define and explore groups, fields, linear spaces, linear maps, and matrix algebras. Such an algebraic structure is defined as a set M with additional properties, for instance, special elements in M, unary operations \(M \to M\) , and associative binary operations \(M \times M \to M\) . We also cover properties of linear spaces such as linear bases, linear independence, and linear maps, followed by advanced topics like duality and topology of finite-dimensional linear spaces. These foundational concepts provide a necessary framework for analyzing the geometric and algebraic relationships intrinsic to Feynman diagrams.