  We study in detail the sensitivity of neutrino oscillation probabilities to
the fundamental neutrino parameters and their possible determination through
experiments. The first part of the paper is devoted to the broad theme of
isolating regions in the neutrino (and anti-neutrino) energy and propagation
length that are sensitive to the oscillation parameters. Such a study is
relevant to neutrinos both from the Earth's atmosphere or from a neutrino
factory. For completeness we discuss the sensitivity, however small, to the
parameters involved in a three-generation framework, and to the Earth matter
density profile. We then study processes relevant to atmospheric neutrinos
which are sensitive to and allow precision measurements of the mixing angle
theta_23 and mass-squared difference delta_32 apart from the mixing angle
theta_13. Crucial to this analysis is charge identification; detectors having
this capability can isolate these matter effects. In particular, we address the
issue of using matter effects to determine whether the mixing angle theta_23 is
maximal, and, if not, to explore how well its octant can be determined. When
realistic detector resolutions are included, we find that deviations of about
15% (20%) from a maximal value of sin^2 theta_23=1/2 can be measured at 95%
(99%) CL provided theta_13 is non-zero, sin^2 theta_13 >= 0.015, and the
neutrino mass ordering is normal, with fairly large exposures of 1000
kton-years.
