I’ve been looking a way to categorize courses in open edx.
I don’t think the current open edx version supports tagging or categorizing. However, the edx website has been using this feature for a while, so if there’s any solution for this, I’d be really grateful for them.
What you’re asking for has more to do with a “marketing site” than the learning experience in itself. We (at https://www.fun-mooc.fr) built an open-source project to make course search and marketing websites in front of Open edX, which has extensive categorization capabilities, integrated with its search engine.
You can find it on GitHub (https://github.com/openfun/richie). If you’re interested in using it and need some pointers, you can reach me on the Open edX slack
The Open edX platform does not have any ready to use UI that allows course filtering and categorizing. This side of the platform is called “Marketing website” and it’s one of the few components that are not Open Source.
The Open edX platform provides APIs with course metadata, filtering, and searching capabilities that you can use to build your own marketing website. You can use Wordpress, Drupal or another CMS in combination with the course-discovery APIs. An alternative is to look at ready to use solutions like the one suggested by @mbenadda.