  This thesis describes capacitance and tunneling experiments performed on
two-dimensional electron gas (2DEG) and quantum dot systems. It develops a
system of equations that allow determination, by means of capacitance
measurements, of the electronic density of states, the electron density, and
the chemical potential in a 2DEG. The thesis describes the use of these
techniques in the observation of a magnetic field induced energy gap to
tunneling in the 2DEG and the single electron addition spectrum in arrays of
quantum dots.
