to attract and hold (somebody's thoughts, attention, affection, etc)
to hold the attention of (somebody); to engross
Her work engages her completely
to induce (somebody) to participate, esp in conversation
to arrange to employ (somebody)
to order (a room, seat, etc) to be kept for one; to reserve
said of a mechanical part: to interlock with (another part)
to enter into contest with (somebody)
engage the enemy fleet
to bring (weapons) together
to pledge or promise (to do something)
to occupy one's time; to participate or become involved
At university he engaged in gymnastics
to enter into conflict
The fleets engaged in the Atlantic
to be or become interlocked or meshed
Middle English engagen from Old French engagier, from en-1 + gage: see gage1. The word originally meant ‘to give something as a pledge’, later ‘to pledge oneself’, hence to become involved in something or with somebody