  We survey an abstract theory of connectivity, based on symmetric submodular
set functions. We start by developing Robertson and Seymour's fundamental
duality between branch decompositions (related to the better-known tree
decompositions) and so-called tangles, which may be viewed as highly connected
regions in a connectivity system. We move on to studying canonical
decompositions of connectivity systems into their maximal tangles. Last, but
not least, we will discuss algorithmic aspect of the theory.
