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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 e ∼ 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 e ∼ 4–8 kpc) with similar effective velocity dispersions. MCGs have elevated rotational support, as evidenced by a strong anticorrelation between the Gauss–Hermite moment h 3 and V / σ. In contrast, 30 |${{\ \rm per\ cent}}$| of control sample galaxies (CSGs) are slow rotators, and fast-rotating CSGs generally show a weak h 3– V / σ anticorrelation. MCGs and CSGs have similar ages, but MCGs are more metal-rich and α -enhanced. Both MCGs and CSGs have shallow negative metallicity gradients and flat [ α /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 and 10 Gyr ago (z ∼ 0.4–2), and had a quiet accretion history since then. This sequence of events might be analogous to, although less extreme than, the compaction events that formed compact quiescent galaxies at z  ∼ 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. [ABSTRACT FROM AUTHOR]