  The search for extrasolar planets is strongly motivated by the goal of
characterizing how frequent habitable worlds and life may be within the Galaxy.
Whilst much effort has been spent on searching for Earth-like planets, large
moons may also be common, temperate abodes for life as well. The methods to
detect extrasolar moons, or "exomoons" are more subtle than their planetary
counterparts and in this thesis I aim to provide a method to find such bodies
in transiting systems, which offer the greatest potential for detection. Before
one can search for the tiny perturbations to the planetary signal, an
understanding of the planetary transit must be established. Therefore, in
Chapters 3 to 5 I discuss the transit model and provide several new insights.
Chapter 4 presents new analytic expressions for the times of transit minima and
the transit duration, which will be critical in the later search for exomoons.
Chapter 5 discusses two sources of distortion to the transit signal, namely
blending (with a focus on the previously unconsidered self-blending scenario)
and light curve smearing due to long integration times. I provide methods to
compensate for both of these effects, thus permitting for the accurate
modelling of the planetary transit light curve. In Chapter 6, I discuss methods
to detect exomoons through their gravitational influence on the host planet,
giving rise to transit timing and duration variations (TTV and TDV). The
previously known TTV effect is updated with a new model and the associated
critical problems are outlined. I then predict a new effect, TDV, which solves
these problems, making exomoon detection viable. Chapter 7 presents a
feasibility study for detecting habitable-zone exomoons with Kepler, where it
is found that moons down to 0.2 Earth masses are detectable. Finally,
conclusions and future work are discussed in Chapter 8.
