Please someone suggest me some reference on the topic "Complex Dynamics". I want a brief geometric treatment from the root level. I have graduate level background on complex analysis, riemannian geometry and topology.

*Dynamics in One Complex Variable*. (AM-160): Third edition (Annals of Mathematics Studies) Jan 22, 2006 by John Milnor

*Complex Dynamics* (Universitext / Universitext: Tracts in Mathematics) Feb 2, 1996
by Lennart Carleson and Theodore Gamelin

*Iteration of Rational Functions*: Complex Analytic Dynamical Systems (Graduate Texts in Mathematics) Oct 1, 1991by Alan F. Beardon

*An Introduction to Chaotic Dynamical Systems*, 2nd Edition (Studies in Nonlinearity) Feb 7, 2003 by Robert Devaney

Milnor's dynamics in one complex variable seems to be a popular choice.

With your background, the book by Milnor or by Beardon looks like a good choice. In addition to the references already suggested, there also are:

MR1224235
Steinmetz, Norbert:

Rational iteration.
Complex analytic dynamical systems. de Gruyter Studies in Mathematics, 16. Walter de Gruyter & Co., Berlin, 1993. x+189 pp. ISBN: 3-11-013765-8

and

MR1747010 Morosawa, S.; Nishimura, Y.; Taniguchi, M.; Ueda, T. Holomorphic dynamics. Translated from the 1995 Japanese original and revised by the authors. Cambridge Studies in Advanced Mathematics, 66. Cambridge University Press, Cambridge, 2000. xii+338 pp. ISBN: 0-521-66258-3

(the latter also introduces some aspects of dynamics in two complex variables).