  We present an estimate of the absolute age of 68 galactic globular clusters
obtained by exploiting the distribution of stars in the full color-magnitude
diagram. In particular, we jointly estimate the absolute age, distance,
reddening, metallicity ([Fe/H]) and [$\alpha$/Fe] of each cluster, imposing
priors motivated by independent observations; we also estimate possible
systematics from stellar modeling. Our derived distances for the globular
cluster sample are in agreement with those obtained from GAIA using
main-sequence dwarf stars (where available), and the inferred ages are in good
agreement with those previously published. The novelty of our approach is that,
with the adopted priors, we are able to estimate robustly these parameters from
the globular cluster color-magnitude diagram. We find that the average age of
the oldest globular clusters is $t_{\rm GC}=13.32 \pm 0.1 {\rm (stat.)} \pm 0.5
{\rm (sys.)}$, at 68\% confidence level, including systematic uncertainties
from stellar modeling. These measurements can be used to infer the age of the
Universe, largely independently of the cosmological parameters: we find an age
of the Universe $t_{\rm U}=13.5^{+0.16}_{-0.14} {\rm (stat.)} \pm 0.5 ({\rm
sys.})$ at 68\% confidence level, accounting for the formation time of globular
clusters and its uncertainty. This value is compatible with $13.8 \pm 0.02$
Gyr, the cosmological model-dependent value inferred by the Planck mission
assuming the $\Lambda$CDM model.
