  [Abridged] The Owens Valley mm-Array has been used to map the CO 1--0
emission in the inner 2'.5 of the grand design spiral galaxy M51 at 2''-3''
resolution. The molecular spiral arms are revealed with unprecedented clarity:
supermassive cloud complexes, Giant Molecular Associations, are for the first
time resolved both along and perpendicular to the arms. Major complexes occur
symmetrically opposite each other in the two major arms. Streaming motions can
be studied in detail along the major and minor axes of M51. The streaming
velocities are very large, 60-150 km/s. For the first time, sufficient
resolution to resolve the structure in the molecular streaming motions is
obtained. Our data support the presence of galactic shocks in the arms of M51.
In general, velocity gradients across arms are higher by a factor of 2-10 than
previously found. They vary in steepness along the spiral arms, becoming
particularly steep in between GMAs. The steep gradients cause conditions of
strong reverse shear in several regions in the arms, and thus the notion that
shear is generally reduced by streaming motions in spiral arms will have to be
modified. Of the three GMAs studied on the SW arm, only one shows reduced
shear. We find an expansion in the NE molecular arm at 25'' radius SE of the
center. This broadening occurs right after the end of the NE arm at the Inner
Lindblad Resonance. Bifurcations in the molecular spiral arm structure, at a
radius of 73'', may be evidence of a secondary compression of the gas caused by
the 4/1 ultraharmonic resonance. Inside the radius of the ILR, we detect narrow
(~ 5'') molecular spiral arms possibly related to the K-band arms found in the
same region. We find evidence of non-circular motions in the inner 20'' which
are consistent with gas on elliptical orbits in a bar.
