A serial killer, as typically defined, is an individual who has murdered three or more people over a period of more than a month, with down time (a "cooling off period") between the murders, and whose motivation for killing is usually based on psychological

Abnormal psychology

Abnormal psychology is the branch of psychology that studies unusual patterns of behavior, emotion and thought, which may or may not be understood as precipitating a mental disorder...

 gratification. Some sources disregard the "three or more" criteria, and define the term as "a series of two or more murders, committed as separate events, usually, but not always, by one offender acting alone" or, including the vital characteristics, a minimum of at least two murders.