  In this thesis we examine methodologies for determining free energy
differences (FEDs) of phases via Monte Carlo simulation. We identify and
address three generic issues that arise in FED calculations; the choice of
representation, the choice of estimator, and the choice of sampling strategy.
In addition we discuss how the classical framework may be extended to take into
account quantum effects.
  Key words: Phase Mapping, Phase Switch, Lattice Switch, Simulated Tempering,
Multi-stage, Weighted Histogram Analysis Method, Fast Growth, Jarzynski method,
Umbrella, Multicanonical, Path Integral Monte Carlo, Path Sampling,
Multihamiltonian, fluctuation theorem
