  In recent decades, the spin and transverse momentum of quarks and gluons were
found to play integral roles in the structure of the nucleon. Simultaneously,
the onset of gluon saturation in hadrons and nuclei at high energies was
predicted to result in a new state of matter dominated by classical gluon
fields. Understanding both of these contributions to hadronic structure is
essential for current and future collider phenomenology. In this Dissertation,
we study the combined effects of transverse spin and gluon saturation using the
Glauber-Gribov-Mueller / McLerran-Venugopalan model of a heavy nucleus in the
quasi-classical approximation. We investigate the use of a
transversely-polarized projectile as a probe of the saturated gluon fields in
the nucleus, finding that the transverse spin asymmetry of produced particles
couples to the component of the gluon fields which is antisymmetric under both
time reversal and charge conjugation. We also analyze the effects of saturation
on the transverse spin asymmetry (Sivers function) of quarks within the wave
function of the nucleus, finding that gluon saturation preferentially generates
the asymmetry through the orbital angular momentum of the nucleons, together
with nuclear shadowing.
