There is no mandatory event in a report program. Events are actually used to organize the statements and control the flow of the program. If the program contains no explicitly defined event blocks, all the statements in the program form the entire event block START-OF-SELECTION. ABAP runtime environment automatically introduces a START-OF-SELECTION at the first [...]

There will be different types of events in ABAP.
Events in Dialog Program
PBO - Process Before Output
PAI - Process After Input
POH - Process on Help
POV - Process on Value Request.
Events in Classical Report
INITIALIZATION
AT SELECTION-SCREEN OUTPUT
AT SELECTION-SCREEN
START-OF–SELECTION.
TOP OF PAGE
END OF PAGE
END-OF-SELECTION.

Control Break events related to Internal Tables
AT NEW FIELD
AT END OF FIELD
AT FIRST
AT LAST
Events in Interactive Report [...]