  This paper presents the mass assembly time scales of nearby galaxies observed
by CALIFA at the 3.5m telescope in Calar Alto. We apply the fossil record
method of the stellar populations to the complete sample of the 3rd CALIFA data
release, with a total of 661 galaxies, covering stellar masses from 10$^{8.4}$
to 10$^{12}$ M$_{\odot}$ and a wide range of Hubble types. We apply spectral
synthesis techniques to the datacubes and process the results to produce the
mass growth time scales and mass weighted ages, from which we obtain temporal
and spatially resolved information in seven bins of galaxy morphology and six
bins of stellar mass (M$_{\star}$) and stellar mass surface density
($\Sigma_{\star}$). We use three different tracers of the spatially resolved
star formation history (mass assembly curves, ratio of half mass to half light
radii, and mass-weighted age gradients) to test if galaxies grow inside-out,
and its dependence with galaxy stellar mass, $\Sigma_{\star}$, and morphology.
Our main results are as follows: (a) The innermost regions of galaxies assemble
their mass at an earlier time than regions located in the outer parts; this
happens at any given M$_{\star}$, $\Sigma_{\star}$, or Hubble type, including
the lowest mass systems. (b) Galaxies present a significant diversity in their
characteristic formation epochs for lower-mass systems. This diversity shows a
strong dependence of the mass assembly time scales on $\Sigma_{\star}$ and
Hubble type in the lower-mass range (10$^{8.4}$ to 10$^{10.4}$), but a very
mild dependence in higher-mass bins. (c) All galaxies show negative
$\langle$log age$\rangle_{M}$ gradients in the inner 1 HLR. The profile
flattens with increasing values of $\Sigma_{\star}$. There is no significant
dependence on M$_{\star}$ within a particular $\Sigma_{\star}$ bin, except for
the lowest bin, where the gradients becomes steeper.
