  In this thesis, we examine the interplay of interstellar dust and gas in the
Andromeda galaxy (M31). In Chapter 2, we use $^{12}$CO CARMA observations of
M31 and dust mass surface density measurements from the Bayesian algorithm
PPMAP to investigate whether the dust emissivity index ($\beta$) is different
inside and outside molecular clouds. We find little difference between the
average $\beta$ inside molecular clouds compared to outside molecular clouds,
in disagreement with models which predict an increase of $\beta$ in dense
environments. In Chapter 3, we use submillimetre observations of M31 at 450 and
850 $\mu$m from the HASHTAG large programme and present first results of the
spatial distribution of dust temperature, $\beta$ and dust mass surface density
from this survey. We search for any excess emission from dust at these
wavelengths and do not find strong evidence for the presence of a sub-mm
excess. In Chapter 4, we produce a new dust-selected cloud catalogue using
archival Herschel observations and HASHTAG observations. We show that dust is a
good tracer of the ISM gas mass at the scale of individual molecular clouds but
with an offset from the combined CO-traced + HI gas masses. In Chapter 5, we
measure the star formation efficiency (SFE) of individual clouds, for the
clouds extracted in Chapter 4, by using FUV+24 $\mu$m emission to trace both
the massive star formation and dust-obscured star formation. We do not find any
systematic trends of SFE with radius but do find strong correlations of the
star formation rate with atomic gas and molecular gas. We find that SFE is
correlated with dust temperature and $\beta$. In Chapter 6, we use a simulated
galaxy to test and optimise the Bayesian algorithm PPMAP for application on
observations of external galaxies. We find an offset between the input
simulation dust mass surface density values and the PPMAP output.
