Not Implemented

The server doesn't support the functionality to fulfill the request.

501 Not Implemented means the server doesn't recognize or support the request method anywhere on the site, as opposed to 405, where the method exists but isn't allowed on that particular resource. You might hit one with an exotic verb the server has never heard of, or from a half-built API where an endpoint is stubbed out but not written yet.

What 501 looks like on the wire

PATCH /records/9 HTTP/1.1
Host: legacy.example.com

HTTP/1.1 501 Not Implemented
Allow: GET, POST, HEAD

About 5xx Server Error

The server failed to fulfill a valid request. The problem is on the server side, not the client.

How to fix 501 Not Implemented

Check the method for typos or verbs the server genuinely doesn't support.
If it's your API, finish or remove the stubbed endpoint that returns it.
Confirm any proxy in front supports the method - some block PATCH or DELETE.

Where it's defined

501 Not Implemented is defined in RFC 9110 §15.6.2. MDN's 501 reference covers browser behavior and examples.