The main goal of these lectures is to explore the intriguing connections, as investigated by Boyd, Deninger, Rodriguez-Villegas, Smyth and others, between Mahler measures of \(A\)-polynomials of hyperbolic \(3\)-manifolds and the special values of \(L\)-functions of Dirichlet characters and elliptic curves.

Our treatment will be mostly expository and proofs will be mostly sketched.