an agreement between two people to marry, or the period of time they are engaged
Tony was stunned when Lisa suddenly broke off their engagement (=finished it).
engagement ring (=a ring that a man gives a woman to show that they are engaged)
an official arrangement to do something, especially one that is related to your work
arrangement to do something[countable]
official/public/royal etc engagement
The princess will continue to carry out royal engagements.
This is his only public speaking engagement on the tour.
His excuse of a prior engagement was accepted.
when you become involved with someone or something in order to understand them
a strategy of engagement and cooperation with China
Many students pass without any real engagement in learning.
fighting between armies etc:
fighting[uncountable and countable] technical
military rules of engagement
an official arrangement to employ or pay someone to do a particular job:
employment[uncountable and countable] formal
Please sign to indicate your acceptance of the terms of engagement.
the fitting together of the working parts of a machine