There are 4 major types
Separately excited
Series excited
Shunt compound
Compound Connection
Separately excited is most common form with most accurate control
Series Excited - Is universal motor so runs on DC or AC - used for car starter motor and dc traction motor, home appliances
Shunt Connection - Can be dangerous two circuits below are connected
Compound Connection - Motor has two winding per field coil. One is connected in parallel with the armature and other in series