This chapter presents the fundamentals used in the mathematical basis of the Finite Element Method. An essential aspect of this scaffolding is the index notation or Einstein notation, which allows the writing of complex and large matrix and tensor expressions in a compact form. Another fundamental aspect, which is at the heart of the method, is the divergence theorems. In its most general form, Green’s Theorem allows transforming domain integrals to boundary integrals, the basis of the boundary element method. Likewise, this chapter deals with the concept of interpolation functions, which allow the approximation of field variables within elements and cells in the domain, using transformations of affine coordinates for this purpose. Related to this are the numerical integration methods of Gauss-Legrende and logarithmic integration, which are fundamental for the numerical approximation of the integrals that appear in the formulation of the method.