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We present a new comprehensive collection of stellar evolutionary tracks and isochrones for rotating low- and intermediate-mass stars assembled with the updated version of PARSEC V2.0. This version includes our recent calibration of the extra mixing from overshooting and rotation, as well as several improvements in nuclear reaction network, treatment of convective zones, mass loss and other physical input parameters. The initial mass of the stellar models covers the range from 0.09 $M_\odot$ to 14 $M_\odot$, for six sets of initial metallicity, from Z=0.004 to Z=0.017. Rotation is considered for stars above $\sim 1 M_\odot$ with a smooth transition between non rotating and extremely fast-rotating models, based on the initial mass. For stars more massive than $\sim 1.3~M_\odot$ the full rotation range, from low to the critical one, is considered. We adopt the solar-scaled chemical mixture by Caffau et al. with Z$_\odot$ = 0.01524. All the evolutionary phases from the pre-main-sequence to the first few thermal-pulses on the asymptotic-giant-branch or central C exhaustion, are considered. The corresponding theoretical isochrones are further derived with TRILEGAL code and are converted in several photometric systems, taking into account different inclination angles. Besides magnitudes, they also offer many other stellar observables in line with the data that are being provided by current large surveys. The new collection is fully integrated in a user friendly WEB interface for the benefit of easily performing stellar population studies.