Functions of bounded variation on RCD spaces

The goal of this manuscript is to provide a comprehensive study of (vector valued) functions of bounded variation defined on RCD spaces, describing their distributional differential and investigating their fine properties and calculus rules. More precisely, this note begins with a recollection of results already present in the literature, some of which are proved in a slightly different way in comparison to the original references: the ideas and techniques used are still the same, but a careful reordering and slight modifications bring to an improvement of the presentation. Then, the bulk of this note contains a collection of results obtained by the author together with coauthors. Improvements about the organization of the results and their proofs, in comparison to the original references, are obtained also in this part.