  We characterized the kinematics, morphology, and stellar population (SP)
properties of a sample of massive compact quiescent galaxies (MCGs) in the
MaNGA Survey (DR15), 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 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.
