  We investigate shear and buoyancy instabilities in radially stratified,
magnetized, cylindrical flows, for application to magnetocentrifugally driven
winds and to magnetized accretion disks. We identify and study nine principal
types of instabilities/overstabilities. When magnetic fields are predominantly
toroidal, as in protostellar winds, the system exhibits axisymmetric
fundamental (FM) and toroidal resonance modes, axisymmetric and
non-axisymmetric toroidal buoyancy (TB) modes, and non-axisymmetric
magnetorotational instability (MRI) modes. Winds with sufficiently steep field
gradients are unstable to the FM, which promotes narrow dense jets in the
centers of wider winds. The TB modes promote small-scale radial mixing. The
MRIs have very low growth rates under low-temperature wind conditions. The
stabilization of buoyancy modes by shear, and of MRIs by compressibility, may
be important in allowing protostellar winds to propagate over vast distances in
space. When magnetic fields are predominantly poloidal, as in winds close to
their source or in astrophysical disks, the system exhibits axisymmetric
Balbus-Hawley (BH), poloidal buoyancy (PB), non-axisymmetric geometric buoyancy
(GPB), and poloidal resonance modes. The BH mode has the fastest growth rate.
The PB mode promotes radial mixing on small scales. The GPB mode at high m is
readily stabilized by shear. We extend previous MRI analyses to focus on
compressibility. We introduce a ``coherent wavelet'' technique to derive
closed-form expressions for instantaneous instability criteria, growth rates,
and net amplification factors for non-axisymmetric MRIs in compressible flows
with both poloidal and toroidal fields. We confirm that these are in excellent
agreement with the results of shearing-sheet temporal integrations.
