Hi Ulrich, I can't speak to the specific Adapt setup but to me it looks like Adapt just customized one of the Moodle themes.

There are a large number of themes you can apply to your Moodle site. Some free ones: https://moodle.org/plugins/browse.php?list=category&id=3 that have some degree of customizability, dependent on the theme.

There also paid ones or you can engage a vendor to create a custom one.

For de Souza Institute, we went with a custom package from a vendor, New School Learning: http://newschoollearning.com/services/ 

But they also sell stock ones: http://newschoollearning.com/themes/  and have an example demo here: http://newschoolnetwork.com/moodle/studio/ 

Moodle is very customizable.. once you have a theme, the key pages you want to look at are the "Default My Home page" settings.. you can add HTML blocks there if you want custom content in it.

Ulrich, I'm guessing you were hoping to shortcut the process of searching through a lot of themes to find this one by asking your question here. However, you might find that theme or another you like in this Moodle News shortlist (http://www.moodlenews.com/2014/22-awesome-moodle-site-themes/), or alternatively you could post your question with a link to the Adapt website in a Moodle forum. The advantage of taking your question to the Moodle Community is that if you need help to customize, you'll already be in the right place.

-Sue