Caligula lived from 12 to 41 A.D. This timeline lists some major events in that time period. Note that this source uses C.E. instead of A.D.
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1. (see the last paragraph): http://en.wikipedia.org/wiki/Caligula
2. (again look at several paragraph toward the end): http://www.roman-empire.net/emperors/caligula.html
NOTE: You discovered he was killed, but you need to see WHY.
He was killed both because he was cruel but also because of his vice. The 1979 movie is good if you can see it.