Cases of the Court of Justice of the European Union (ECJ) and those of the Court of First Instance are published in Reports of Cases before the Court of Justice and Court of First Instance at KJE924.5 R47 (Basement). Because there is a backlog of several months between the judgment and its publication in the Reports, you may want to check the ECJ's Web site (http://curia.europa.eu), which posts cases within a few days after judgment. The ECJ's site includes case law from 1997 to present. EUR-Lex (https://eur-lex.europa.eu/collection/eu-law/eu-case-law.html) also provides access EU case law, including earlier decisions. In addition, EUR-Lex allows for searching by search terms and provides citation information.
Commercial reporters also publish selected cases of the ECJ and of national courts' decisions on issues of community or EU law. Try European Community Cases at KJE923.7 .E97 and Common Market Law Reports at KJE923.7 .C66 (Annex-3rd).
Both Westlaw (EU-CS) and Lexis (ECJ) provide access to ECJ cases from 1954 to present.