Modular forms are a certain kind of holomorphic maps defined on the upper half-plane whose Fourier expansions, very much surprisingly, mantain an intimate relationship with number theory. One of the most striking and intricate manifestations of this relationship is the proof by Andrew Wiles and others of Fermat's Last Theorem, a result about an integral equation with 4 variables which resisted proof for over 350 years. Eisenstein series are a particular kind of modular forms which can be written down explicitly, thus being ideal for experimentation in the theory of modular forms. In this talk I will give some examples of Eisenstein series, and we will witness exactly how number theoretic information can be extracted from their structure.