  We measure $\lambda_{R_e}$, a proxy for galaxy specific stellar angular
momentum within one effective radius, and the ellipticity, $\epsilon$, for
about 2300 galaxies of all morphological types observed with integral field
spectroscopy as part of the MaNGA survey, the largest such sample to date. We
use the $(\lambda_{R_e}, \epsilon)$ diagram to separate early-type galaxies
into fast and slow rotators. We also visually classify each galaxy according to
its optical morphology and two-dimensional stellar velocity field. Comparing
these classifications to quantitative $\lambda_{R_e}$ measurements reveals
tight relationships between angular momentum and galaxy structure. In order to
account for atmospheric seeing, we use realistic models of galaxy kinematics to
derive a general approximate analytic correction for $\lambda_{R_e}$. Thanks to
the size of the sample and the large number of massive galaxies, we
unambiguously detect a clear bimodality in the $(\lambda_{R_e}, \epsilon)$
diagram which may result from fundamental differences in galaxy assembly
history. There is a sharp secondary density peak inside the region of the
diagram with low $\lambda_{R_e}$ and $\epsilon < 0.4$, previously suggested as
the definition for slow rotators. Most of these galaxies are visually
classified as non-regular rotators and have high velocity dispersion. The
intrinsic bimodality must be stronger, as it tends to be smoothed by noise and
inclination. The large sample of slow rotators allows us for the first time to
unveil a secondary peak at +/-90 degrees in their distribution of the
misalignments between the photometric and kinematic position angles. We confirm
that genuine slow rotators start appearing above a stellar mass of
2\times10^{11} M_{\odot}$ where a significant number of high-mass fast rotators
also exist.
