  Using high resolution spectra from the VLT LEGA-C program, we reconstruct the
star formation histories (SFHs) of 607 galaxies at redshifts $z = 0.6-1.0$ and
stellar masses $\gtrsim10^{10}$M$_{\odot}$ using a custom full spectrum fitting
algorithm that incorporates the emcee and FSPS packages. We show that the
mass-weighted age of a galaxy correlates strongly with stellar velocity
dispersion ($\sigma_*$) and ongoing star-formation (SF) activity, with the
stellar content in higher-$\sigma_*$ galaxies having formed earlier and faster.
The SFHs of quiescent galaxies are generally consistent with passive evolution
since their main SF epoch, but a minority show clear evidence of a rejuvenation
event in their recent past. The mean age of stars in galaxies that are
star-forming is generally significantly younger, with SF peaking after $z<1.5$
for almost all star-forming galaxies in the sample: many of these still have
either constant or rising SFRs on timescales $>100$Myrs. This indicates that
$z>2$ progenitors of $z\sim1$ star-forming galaxies are generally far less
massive. Finally, despite considerable variance in the individual SFHs, we show
that the current SF activity of massive galaxies ($>$L$_*$) at $z\sim1$
correlates with SF levels at least $3$Gyrs prior: SFHs retain `memory' on a
large fraction of the Hubble time. Our results illustrate a novel approach to
resolve the formation phase of galaxies, and in identifying their individual
evolutionary paths, connects progenitors and descendants across cosmic time.
This is uniquely enabled by the high-quality continuum spectroscopy provided by
the LEGA-C survey.
