  We present the catalog of RR Lyrae stars discovered in a 4.5 square degrees
area in the central parts of the Large Magellanic Cloud (LMC). Presented sample
contains 7612 objects, including 5455 fundamental mode pulsators (RRab), 1655
first-overtone (RRc), 272 second-overtone (RRe) and 230 double-mode RR Lyr
stars (RRd). Additionally we attach a list of several dozen other short-period
pulsating variables. The catalog data include astrometry, periods, BVI
photometry, amplitudes, and parameters of the Fourier decomposition of the
I-band light curve of each object.
  We present density map of RR Lyr stars in the observed fields which shows
that the variables are strongly concentrated toward the LMC center. The modal
values of the period distribution for RRab, RRc and RRe stars are 0.573, 0.339
and 0.276 days, respectively. The period-luminosity diagrams for BVI magnitudes
and for extinction insensitive index W_I are constructed. We provide the
logP-I, logP-V and logP-W_I relations for RRab, RRc and RRe stars. The mean
observed V-band magnitudes of RR Lyr stars in the LMC are 19.36 mag and 19.31
mag for ab and c types, respectively, while the extinction free values are
18.91 mag and 18.89 mag.
  We also found a large number of RR Lyr stars pulsating in two modes closely
spaced in the power spectrum. We discovered three stars which simultaneously
reveal RR Lyr-type and eclipsing-type variability. If any of these objects were
an eclipsing binary system containing RR Lyr star, then for the first time the
direct determination of the mass of RR Lyr variable would be possible.
  We also provide a list of six LMC star clusters which contain RR Lyr stars.
The richest cluster, NGC 1835, hosts 84 RR Lyr variables.
