We introduce a new generation of PARSEC – COLIBRI stellar isochrones that include a detailed treatment of the thermally-pulsing asymptotic giant branch ( TP-AGB ) phase , and covering a wide range of initial metallicities ( 0.0001 < \mbox { $Z \mbox { $ { } _ { i } $ } $ } < 0.06 ) . Compared to previous releases , the main novelties and improvements are : use of new TP-AGB tracks and related atmosphere models and spectra for M and C-type stars ; inclusion of the surface H+He+CNO abundances in the isochrone tables , accounting for the effects of diffusion , dredge-up episodes and hot-bottom burning ; inclusion of complete thermal pulse cycles , with a complete description of the in-cycle changes in the stellar parameters ; new pulsation models to describe the long-period variability in the fundamental and first overtone modes ; new dust models that follow the growth of the grains during the AGB evolution , in combination with radiative transfer calculations for the reprocessing of the photospheric emission . Overall , these improvements are expected to lead to a more consistent and detailed description of properties of TP-AGB stars expected in resolved stellar populations , especially in regard to their mean photometric properties from optical to mid-infrared wavelengths . We illustrate the expected numbers of TP-AGB stars of different types in stellar populations covering a wide range of ages and initial metallicities , providing further details on the “ C-star island ” that appears at intermediate values of age and metallicity , and about the AGB-boosting effect that occurs at ages close to 1.6-Gyr for populations of all metallicities . The isochrones are available through a new dedicated web server .