  The Mahler measure of a monic polynomial $P(x) = a_dx^d + a_{d-1}x^{d-1} +
\dots + a_1x + a_0$ is defined as $M(P) := |a_d| \prod_{P(\alpha)=0} \max\{1,
|\alpha|\}$, where the product runs over all roots of $P$. Lehmer's problem
asks whether there exists a constant $C>1$ such that $M(P) \geq C$ for all
noncyclotomic polynomials in $\mathbb{Z}[x]$. In this thesis, we examine the
properties of various integer sequences related to this problem, with special
focus on how these sequences might help solving Lehmer's problem.
