In this lecture notes, we aim at giving an introduction to the K\"ahler-Ricci
flow (KRF) on Fano manifolds. It covers some of the developments of the KRF in
its first twenty years (1984-2003), especially an essentially self-contained
exposition of Perelman's uniform estimates on the scalar curvature, the
diameter, and the Ricci potential function for the normalized K\"ahler-Ricci
flow (NKRF), including the monotonicity of Perelman's \mu-entropy and
\kappa-noncollapsing theorems for the Ricci flow on compact manifolds.
The Notes is based on a mini-course on KRF delivered at University of
Toulouse III in February 2010, a talk on Perelman's uniform estimates for NKRF
at Columbia University's Geometry and Analysis Seminar in Fall 2005, and
several conference talks, including "Einstein Manifolds and Beyond" at CIRM
(Marseille - Luminy, fall 2007), "Program on Extremal K\"ahler Metrics and
K\"ahler-Ricci Flow" at the De Giorgi Center (Pisa, spring 2008), and "Analytic
Aspects of Algebraic and Complex Geometry" at CIRM (Marseille - Luminy, spring
2011).Comment: v.2: corrected a number of typos and added the proof of Theorem 2.3
on preserving positive orthogonal bisectional curvature. To appear as a book
chapter in An Introduction to the K\"ahler-Ricci Flow, Lecture Notes in
Mathematics, vol. 2086, Springer, 201
