  We characterized the kinematics, morphology, and stellar population (SP)
properties of a sample of massive compact quiescent galaxies (MCGs, $10
\lesssim \log M_\star$/$M_\odot \lesssim 11$ and $r_{\rm e} \sim 1-3 $kpc) in
the MaNGA Survey, with the goal of constraining their formation, assembly
history and assessing their relation with non-compact quiescent galaxies. We
compared their properties with those of a control sample of median-sized
quiescent galaxies ($r_{\rm e} \sim 4-8 $kpc) with similar effective velocity
dispersions. MCGs have elevated rotational support, as evidenced by a strong
anti-correlation between the Gauss-Hermite moment $h_3$ and $V/\sigma$. In
contrast, 30$\%$ of control sample galaxies (CSGs) are slow rotators, and
fast-rotating CSGs generally show a weak $h_3-V/\sigma$ anti-correlation. MCGs
and CSGs have similar ages, but MCGs are more metal-rich and $\alpha$-enhanced.
Both MCGs and CSGs have shallow negative metallicity gradients and flat
[$\alpha$/Fe] gradients. On average, MCGs and CSGs have flat age gradients, but
CSGs have a significantly larger dispersion of gradient values. The kinematics
and SP properties of MCGs suggest that they experienced highly-dissipative
gas-rich events, such as mergers, followed by an intense, short, and centrally
concentrated burst of star formation, between 4 to 10 Gyr ago ($z\sim0.4-2$),
and had a quiet accretion history since then. This sequence of events might be
analogous to, although less extreme than, the compaction events which formed
compact quiescent galaxies at $z \sim 2$. The small sizes of MCGs, and the high
efficiency and short duration of their last star formation episode suggest that
they are descendants of compact post-starburst galaxies.
