I bought settlers 3: ultimate collection today, and I cannot play it because it requires a serial number. Can somebody tell me how to get one please?

Meta.

Open your library (https://www.gog.com/account)
Click on the the picture of the game
More (https://i.imgur.com/xI0LBrS.jpg)
Serial Keys

Note:
You have to use a regular normal web browser.
GOG Galaxy never show serial numbers.

It always struck me as bizarre that it can't do this... after all, the main part of Galaxy is basically a web browser. The fact you can't see your serials in Galaxy prevents it from being self contained. You can buy the games, install the games and launch the games all within Galaxy but you need to open the site in a browser to get your serial key. Out of interest, do you mean the game won't run at all without the serial key or is it just multiplayer you can't get access to?

My Serial Number for Settlers 3: Ultimate Edition isnt working.

You could try suggestions from this thread
https://www.gog.com/forum/the_settlers_series/settlers_3_serial_key

I can't publish any links on this forum for some reason, but go here:
support[DOT]gog.com/hc/en-us/articles/360008480314-Settlers-3-Ultimate-Collection-Game-asks-for-CD-Key-in-sing leplayer-mode?product=gog

For what fuckin reason Keys are depleted and they still sell the f...game?

They sell those games to people who don't care about keys/multiplayer, like me.

I have recently bought the game. The game's UI (In GOG.com) says all keys are depleted.
I previously used a key and forgot where I found it.

Where can I get another?

You wait a bit for GOG to replenish them.

This link has the key I used.
I no longer require one but thank you for you reply!

https://www.gog.com/forum/the_settlers_series/settlers_3_serial_key