How can I show the week numbers in the calendar shown at the top in GNOME Shell?

If you have dconf Editor, launch it and navigate to /org/gnome/desktop/calendar/show-weekdate. Then disable Use default value and set Custom value to True.

Alternatively just open Terminal and run

gsettings set org.gnome.desktop.calendar show-weekdate true

You can do that with the GNOME Tweak Tool.

sudo apt update
sudo apt install gnome-tweak-tool

Open the application after installing it.

  1. Go to the "Top Bar" menu item from left.

    Ubuntu Tweak Tool

  2. There's an option called "Show week numbers". Check it.

    Calendar with week numbers