This chapter introduces the Green’s function technique, and illustrates some basic results which stem from solving Maxwell’s equations in this new way. The Green’s functions method can be used, in principle, to solve any linear PDE with constant coefficients. It can be looked at as a practical way to implement the superposition principle. Those readers who are interested in a more general overview of this subject should consult a treatise; still, it may be useful to outline the basic features of the method. The chapter discusses the orthonormal basis functions, and the Green’s function in this basis. Green’s function is still possible, but more delicate. It shows that the reader knows already at least the fundamentals of distribution theory. The chapter examines more advisable to concentrate on two examples of high practical relevance, namely spherical and cylindrical harmonics.