Breast cancer is a clinically and molecularly heterogeneous disease displaying distinct therapeutic responses. Although recent studies have explored the genomic and transcriptomic landscapes of breast cancer, the epigenetic architecture has received less attention.

To address this, an optimised Reduced Representation Bisulfite Sequencing protocol was performed on 1482 primary breast tumours (and 237 matched adjacent normal tissues). This constitutes the largest breast cancer methylome yet, and this thesis describes the bioinformatics and statistical analysis of this study.

Noticeable epigenetic drift (both gain and loss of homogeneous DNA methylation patterns) was observed in breast tumours when compared to normal tissues, with markedly higher differences in late replicating genomic regions. The extent of epigenetic drift was also found to be highly heterogeneous between the breast tumours and was sharply correlated with the tumour’s mitotic index, indicating that epigenetic drift is largely a consequence of the accumulation of passive cell division related errors.

A novel algorithm called DMARC (Directed Methylation Altered Regions in Cancer) was developed that utilised the tumour-specific drift rates to discriminate between methylation alterations attained as a consequence of stochastic cell division errors ($background$) and those reflecting a more instructive biological process ($directed$). Directed methylation alterations were significantly enriched for gene expression changes in breast cancer, compared to background alterations. Characterising these methylation aberrations with gene expression led to the identification of breast cancer subtype-specific epigenetic genes with consequences on transcription and prognosis.

Cancer genes may be deregulated by multiple mechanisms. By integrating with existing copy number and gene expression profiles for these tumours, DNA methylation alterations were revealed as the predominant mechanism correlated with differentially expressed genes in breast cancer. The crucial role of DNA methylation as a mechanism to target the silencing of specific genes within copy number amplifications is also explored which led to the identification of a putative tumour suppressor gene, $THSZ2$.

Finally, the first genome-wide assessment of epigenomic evolution in breast cancer is conducted. Both, the level of intratumoural heterogeneity, and the extent of epiallelic burden were found to be prognostic, and revealed an extraordinary distinction in the role of epiclonal dynamics in different breast cancer subtypes.

Collectively, the results presented in this thesis have shed light on the somatic DNA methylation basis of inter-patient as well as intra-tumour heterogeneity in breast cancer. This complements our genetic knowledge of the disease, and will help move us towards tailoring treatments to the patient's molecular profile.