  We present a numerical lattice quantum chromodynamics calculation of
isovector form factors and the first few moments of the isovector structure
functions of the nucleon. The calculation employs two degenerate dynamical
flavors of domain-wall fermions, resulting in good control of chiral symmetry
breaking. Non-perturbative renormalization of the relevant quark currents is
performed where necessary. The inverse lattice spacing, $a^{-1}$, is about 1.7
GeV. We use degenerate up and down dynamical quark masses around 1, 3/4 and 1/2
the strange quark mass. The physical volume of the lattice is about
$(1.9{fm})^3$. The ratio of the isovector vector to axial charges, $g_A/g_V$,
trends a bit lower than the experimental value as the quark mass is reduced
toward the physical point. We calculate the momentum-transfer dependences of
the isovector vector, axial, induced tensor and induced pseudoscalar form
factors. The Goldberger-Treiman relation holds at low momentum transfer and
yields a pion-nucleon coupling, $g_{\pi NN} = 15.5(1.4)$, where the quoted
error is only statistical. We find that the flavor non-singlet quark momentum
fraction $<x>_{u-d}$ and quark helicity fraction $<x>_{\Delta u-\Delta d}$
overshoot their experimental values after linear chiral extrapolation. We
obtain the transversity, $<1 >_{\delta u-\delta d} = 0.93(6)$ in $\bar{\rm MS}$
at 2 GeV and a twist-3 polarized moment, $d_1$, appears small, suggesting that
the Wandzura-Wilczek relation holds approximately. We discuss the systematic
errors in the calculation, with particular attention paid to finite-volume
effects, excited-state contamination, and chiral extrapolations.
