Variational methods refer to proofs established by showing that a suitable auxiliary function attains a minimum or has a critical point. Although relatively technical, this text is appropriate for the beginning of graduate studies for a student willing to get familiar with Variational Analysis and its application in Differential Equations. The text is organised in a way to provide the required tools and to lead the reader to a complete understanding of the concept. Student from the physical sciences will also gain non-negligible knowledge since Variational methods can be viewed as a mathematical form of the principle of least action in Physics.