The definition of the Kauffman bracket skein algebra of an oriented surface was originally motivated by the Jones polynomial, and a representation of the skein algebra features importantly in the topological quantum field theory description of Witten's 3-manifold invariant. Later, the skein algebra of a surface was found to bear deep relationships to hyperbolic geometry, via the SL2C-character variety. We will explicate this relationship between the skein algebra and the hyperbolic geometry of a surface, using representations.