The objective of these lectures is to demonstrate a unifying role played by the property of absolute continuity in understanding the behaviour of, and construction of effective algorithms to explore, probability measures in high and infinite dimensional spaces. Furthermore links to continuo time processes, and SPDEs in particular, will be made. These attached notes outline the structure of the lectures, and give various references to the literature that I will not, for reasons of brevity, give in full during the lectures themselves. These also include references to related material that I will not have time to cover in the lectures at all.