After the successful Run I of the Tevatron (1992-1996), with the
top quark discovery, both CDF and D0 experiments were extensively upgraded
to meet the challenges of the Tevatron Run II collider.  The energy of p anti-p
collisions at the Tevatron was increased from s**(1/2) = 1.8 TeV to s**(1/2) =
1.96 TeV.  tt-bar production cross section is expected to increase by a
factor of ~ 30%.  Major upgrades in the Tevatron accelerator chain will
increase the Run II instantaneous luminosity: the goal is to achieve L = 5 -
20 x 1031 cm2 s-1 while the highest luminosity reached up to now
(September 2003) is 5.2 x 1031 cm2 s-1.

In this paper we will present the top quark properties measured by both CDF
and D0 with the first physics-quality data collected during the Run II
(March 2002-January 2003).  First we will review tt-bar cross section
measurements in the various decay channels; then top quark mass measurements
will be presented.