Abstract: Given a surface $F$, the cylinder over the surface is the Cartesian product of $F$ and the unit interval. The skein module of $F \times [0,1]$ is formed by considering the kinds of knots and links that can exist inside this manifold. By stacking two copies of $F \times [0,1]$ together, we can define a multiplication on the skein module to create the skein algebra of $F$, denoted $K(F)$. We will look at the skein algebra of the annulus, the torus, and the genus two surface. In particular, we will investigate the commutators of the skein algebras of the torus and the genus two surface using the non-separating simple closed curves on those surfaces.