  We present new B, V and I CCD time-series photometry for 177 variable stars
in a 13'X 13' field centered on the globular cluster M54 (lying at the center
of the Sagittarius dwarf spheroidal galaxy), 94 of which are newly identified
variables. The total sample is composed of 2 anomalous Cepheids, 144 RR Lyrae
stars (108 RR0 and 36 RR1), 3 SX Phoenicis, 7 eclipsing binaries (5 W UMA and 2
Algol binaries), 3 variables of uncertain classification and 18 long-period
variables. The large majority of the RR Lyrae variables likely belong to M54.
Ephemerides are provided for all the observed short-period variables. The
pulsational properties of the M54 RR Lyrae variables are close to those of
Oosterhoff I clusters, but a significant number of long-period ab type RR Lyrae
are present. We use the observed properties of the RR Lyrae to estimate the
reddening and the distance modulus of M54, E(B-V)=0.16 +/- 0.02 and
(m-M)_0=17.13 +/- 0.11, respectively, in excellent agreement with the most
recent estimates. The metallicity has been estimated for a subset of 47 RR
Lyrae stars, with especially good quality light curves, from the Fourier
parameters of the V light curve. The derived metallicity distribution has a
symmetric bell shape, with a mean of <[Fe/H]>=-1.65 and a standard deviation
sigma=0.16 dex. Seven stars have been identified as likely belonging to the
Sagittarius galaxy, based on their too high or too low metallicity. This
evidence, if confirmed, might suggest that old stars in this galaxy span a wide
range of metallicities.
