One of the biggest difficulties with researching the EU is that there is a lot of material in a lot of places; while much of it overlaps, some of it does not. It is highly likely that your challenge in research will come from deciding exactly where you should be looking for what - use this information here to help you plan your research.
If you have a particular treaty or regime in mind, search in the law library catalog for books by keyword using the name plus the word commentary. A commentary is a particular type of book that analyzes a legal instrument article-by-article, has extensive footnotes to other secondary sources and case law, and usually contains extensive history or purpose notes. For example -
For more guidance on finding books, see the Books section of this guide.
Research Guide to Instruments of European Regional Organizations by 
European Union Law, Including Brexit and Beyond, in a Nutshell by