  We study the Schr\"{o}dinger operator describing a two-dimensional quantum
particle moving in presence of $ N \geqslant 1 $ Aharonov-Bohm magnetic fluxes.
We classify all the self-adjont realizations of such an operator, providing an
explicit characterization of their domains and actions. Moreover, we examine
their spectral and scattering properties, proving in particular the existence
and completeness of wave operators in relation with the free dynamics.
