  In this paper, we study the deformations of Kolyvagin systems that are known
to exist in a wide variety of cases, by the work of B. Howard, B. Mazur, and K.
Rubin for the residual Galois representations, along the cyclotomic Iwasawa
algebra. We prove, under certain technical hypotheses, that a cyclotomic
deformation of a Kolyvagin system exists. We also briefly discuss how our
techniques could be extended to prove that one could deform Kolyvagin systems
for other deformations as well.
  We discuss several applications of this result, particularly relation of
these $\Lambda$-adic Kolyvagin systems to p-adic L-functions (in view of the
conjectures of Perrin-Riou on p-adic L-functions) and applications to main
conjectures; also applications to the study of Iwasawa theory of Rubin-Stark
units.
