  Based on the analogies between knot theory and number theory, we study a
deformation theory for SL_2-representations of knot groups, following after
Mazur's deformation theory of Galois representations. Firstly, by employing the
pseudo-SL_2-representations, we prove the existence of the universal
deformation of a given SL_2-representation of a finitely generated group Pi
over a field whose characteristic is not 2. We then show its connection with
the character scheme for SL_2-representations of Pi when k is an algebraically
closed field. We investigate examples concerning Riley representations of
2-bridge knot groups and give explicit forms of the universal deformations.
Finally we discuss the universal deformation of the holonomy representation of
a hyperbolic knot group in connection with Thurston's theory on deformations of
hyperbolic structures.
