  This paper presents the results of a dense and intensive X-ray and optical
monitoring of the narrow-line Seyfert 1 galaxy NGC 4051 carried out in 2000.
Results of the optical analysis are consistent with previous measurements. The
amplitude of optical emission line variability is a factor of two larger than
that of the underlying optical continuum, but part or all of the difference can
be due to host-galaxy starlight contamination or due to the lines being driven
by the unseen UV continuum, which is more variable than the optical continuum.
We measured the lag between optical lines and continuum and found a lower, more
accurate broad line region size of 3.0+-1.5 light days in this object. The
implied black hole mass is M_BH=5(+6,-3)x10^5 M_sun; this is the lowest mass
found, so far, for an active nucleus. We find significant evidence for an
X-ray-optical (XO) correlation with a peak lag of about <1 day, although the
centroid of the asymmetric correlation function reveals that part of the
optical flux varies in advance of the X-ray flux by 2.4+-1.0 days. This complex
XO correlation is explained as a possible combination of X-ray reprocessing and
perturbations propagating from the outer (optically emitting) parts of the
accretion disc into its inner (X-ray emitting) region.
