  We present two different representations of (1,1)-knots and study some
connections between them. The first representation is algebraic: every
(1,1)-knot is represented by an element of the pure mapping class group of the
twice punctured torus. The second representation is parametric: every
(1,1)-knot can be represented by a 4-tuple of integer parameters. The strict
connection of this representation with the class of Dunwoody manifolds is
illustrated. The above representations are explicitly obtained in some
interesting cases, including two-bridge knots and torus knots.
