  Nucleon structure study is one of the most important research areas in modern
physics and has challenged us for decades. Spin has played an essential role
and often brought surprises and puzzles to the investigation of the nucleon
structure and the strong interaction. New experimental data on nucleon spin
structure at low to intermediate momentum transfers combined with existing high
momentum transfer data offer a comprehensive picture in the strong region of
the interaction and of the transition region from the strong to the
asymptotic-free region. Insight for some aspects of the theory for the strong
interaction, Quantum Chromodynamics (QCD), is gained by exploring lower moments
of spin structure functions and their corresponding sum rules. These moments
are expressed in terms of an operator-product expansion using quark and gluon
degrees of freedom at moderately large momentum transfers. The higher-twist
contributions have been examined through the evolution of these moments as the
momentum transfer varies from higher to lower values. Furthermore, QCD-inspired
low-energy effective theories, which explicitly include chiral symmetry
breaking, are tested at low momentum transfers. The validity of these theories
is further examined as the momentum transfer increases to moderate values. It
is found that chiral perturbation theory calculations agree reasonably well
with the first moment of the spin structure function g_1 at low momentum
transfer of 0.05 - 0.1 GeV^2 but fail to reproduce some of the higher moments,
noticeably, the neutron data in the case of the generalized polarizability
Delta_LT. The Burkhardt-Cottingham sum rule has been verified with good
accuracy in a wide range of Q^2 assuming that no singular behavior of the
structure functions is present at very high excitation energies.
