  We present the results from $VI$ CCD time-series photometry of the globular
cluster M13 (NGC 6205). From the Fourier decomposition of the light curves of
RRab and RRc stars we found an average metallicity of [Fe/H]zw = -1.58 $\pm$
0.09. The distance to the cluster was estimated as 7.1 $\pm$ 0.1 kpc from
independent methods related to the variable star families RR Lyrae, SX Phe and
W Virginis, from the luminosity of the theoretical ZAHB and from the orbit
solution of a newly discovered contact binary star. The RR Lyrae pulsation
modes are segregated by the red edge of the first overtone instability strip in
this OoII type cluster. A membership analysis of 52,800 stars in the field of
the cluster is presented based on \textit{Gaia}-DR2 proper motions which
enabled the recognition of 23,070 likely cluster members, for 7,630 of which we
possess $VI$ photometry. The identification of member stars allowed the
construction of a clean CMD and a proper ZAHB and isochrone fitting, consistent
with a reddening, age and distance of 0.02 mag, 12.6 Gyrs and 7.1 kpc
respectively. We report seven new variables; one RRc, two SX Phe stars, three
SR and one contact binary. V31 presents double-mode nature and we confirm V36
as RRd. Fifteen variable star candidates are also reported. The analysis of
eighteen stars in the field of the cluster, reported as RR Lyrae from the
$Gaia$-DR2 data base reveals that at least seven are not variable. We noted the
presence of a high velocity star in the field of the cluster.
