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 ± 0.09. The distance to the cluster was estimated as 7.1 ± 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 Gaia-DR2 proper motions which enabled the recognition of 23 070 likely cluster members, for 7630 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 Gyr 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. 15 variable star candidates are also reported. The analysis of 18 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.