Section 16.3: AC Commutator Motors
The universal motor is essentially a series (DC) motor with a laminated field structure (to reduce the hysteresis and eddy-current losses resulting from its applied AC voltage)
Because its field circuit in series with armature circuit ...
It runs when supplied with AC voltage because …
When the applied voltage reverses polarity (during its negative half cycle), both the armature current and the field current (and hence the field flux) reverse direction resulting in unidirectional torque on the armature during both the AC’s positive and negative half cycles
See text pp. 582-584 for further details)