Notice period
The time you're contractually required to keep working after resigning — two weeks by convention in the US, one to three months by contract in much of Europe.
In the US, two weeks is a norm rather than a legal requirement. In the UK, Germany, the Netherlands and much of the EU it's a contractual term, commonly one to three months and sometimes longer for senior roles, and it is enforceable.
It's a negotiating item in both directions. New employers with a start date in mind will sometimes wait, and sometimes offer a signing bonus to cover a shortfall. Current employers will sometimes release you early, particularly if there's little handover left. Neither happens unless asked.
Plan the sequence backwards from it. A three-month notice period means the offer conversation, the resignation, and the start date span an entire quarter — and it's the most common reason a candidate who interviewed well loses a role to someone available sooner. Say it early rather than at offer stage.
Offer letter
The written document stating the terms of employment — and the only version of the offer that binds anyone.
Searching while employed
Running a job search without your current employer finding out — which mostly comes down to controlling signals rather than keeping secrets.