An Introduction to A-polynomials and their Mahler Measures

These are the notes of the three lectures I delivered at the mini-workshop "Knot Theory and Number Theory around the A-Polynomial" at the Instituto Superior Tecnico (IST) in Lisbon in January 2014. The goal of the lectures was to familiarize, both the author and, the audience with the A-polynomials and the connection between the Mahler measures of A-polynomials and volumes. The style of these notes is expository, written informally with the aim of giving a flavor of the subject with ample amount of references to direct the interest readers to the details.