In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they 'run round' a singularity. As the name implies, the fundamental meaning of monodromy comes from 'running round singly'. It is closely associated with covering maps and their degeneration into ramification; the aspect giving rise to monodromy phenomena is that certain functions we may wish to define fail to be single-valued as we 'run round' a path encircling a singularity. The failure of monodromy is best measured by defining a monodromy group: a group of transformations acting on the data that encodes what does happen as we 'run round'.