In this chapter, we introduce several well-known concepts and results from real, functional, and matrix analysis. These include function spaces, inequalities, embedding and interpolation theorems, Fourier transforms and convolutions, Dirichlet and Fejér kernels and singular integrals, Schatten classes and norms of compact operators, and congruent and reproducing kernel Hilbert spaces. Additionally, we present technical results concerning the properties of slowly and regularly varying functions, which are essential for stating and proving the results in this text.