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We present the results from $VI$ CCD time-series photometry of the globularcluster M13 (NGC 6205). From the Fourier decomposition of the light curves ofRRab 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 fromindependent methods related to the variable star families RR Lyrae, SX Phe andW Virginis, from the luminosity of the theoretical ZAHB and from the orbitsolution of a newly discovered contact binary star. The RR Lyrae pulsationmodes are segregated by the red edge of the first overtone instability strip inthis OoII type cluster. A membership analysis of 52,800 stars in the field ofthe cluster is presented based on \textit{Gaia}-DR2 proper motions whichenabled the recognition of 23,070 likely cluster members, for 7,630 of which wepossess $VI$ photometry. The identification of member stars allowed theconstruction of a clean CMD and a proper ZAHB and isochrone fitting, consistentwith a reddening, age and distance of 0.02 mag, 12.6 Gyrs and 7.1 kpcrespectively. We report seven new variables; one RRc, two SX Phe stars, threeSR and one contact binary. V31 presents double-mode nature and we confirm V36as RRd. Fifteen variable star candidates are also reported. The analysis ofeighteen 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 thepresence of a high velocity star in the field of the cluster.

A new study of the variable star population in the Hercules globular cluster (M13; NGC 6205)