  In this thesis, I analyse the 2D anisotropic Baryon Acoustic Oscillation
(BAO) signal present in the final WiggleZ dataset. I utilise newly released
covariance matrices from the WizCOLA simulations and follow well tested
methodologies used in prior analyses of the BAO signal in alternative datasets.
The WiggleZ data is presented in two forms - in multipole expansion and in data
wedges - both of which are analysed in this thesis. I test my model against
previous one dimensional analyses of the BAO signal in the WiggleZ data and
against WizCOLA simulations, and find it to be free of bias or systematic
offsets. However, the analysis on the wedge data format was unable to properly
constrain cosmological parameters, and thus discarded in favour of the
multipole analysis. The multipole analysis determined $\Omega_c h^2$, $H(z)$
and $D_A(z)$ for three redshift bins, of effective redshifts $z = 0.44, 0.60$
and $0.73$. The respective constraints on $\Omega_c h^2$ are
$0.119^{+0.029}_{-0.026}$, $0.151^{+0.038}_{-0.025}$ and
$0.140^{+0.036}_{-0.022}$. The fits for $H(z)$ are respectively $87 \pm 16$,
$90 \pm 15$ and $82 \pm 13$ km s$^{-1}$ Mpc$^{-1}$, and for $D_A(z)$ I find
values of $1300 \pm 160$, $1300 \pm 180$ and $1350 \pm 160$ Mpc. These
cosmological constraints are consistent with Flat $\Lambda$CDM cosmology.
