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1. To inform one's employer of one's resignation. In this usage, a possessive pronoun is often used between "give" and "notice." I just gave my notice, so I'm officially leaving in two weeks. You can just walk out—you have to at least give notice!
2. To alert one to something. I think your teacher would have been more understanding if you had given notice of this printing issue in advance.
give (one's) notice
to formally tell one's employer that one is quitting one's job. Did you hear that James is leaving? He gave his notice yesterday. Lisa gave notice today. She got a job offer from another company.
1. Inform or warn someone of something, as in He's prompt about giving us notice of any discrepancy in the accounts. [Late 1500s]
2. Tell one's employer one is quitting, as in Our housekeeper gave notice last week. This usage, first recorded in 1765, originally alluded to any kind of termination, such as a housing lease, but today is most often used for leaving employment.