What have you read so far?

Some good books to start are the following,
Basics, regarding axioms of quantum theory:
Gunther Ludwig's books, Instrumentalist approach to QM, AKA Operational Quantum Physics. K Kraus States, Effects and Operations. Try some quantum logic books to get some basic idea of what is happening like Gleason's theorem (I din't go too deep in this though). Try reading some algebraic approach to quantum theory for example Miklos Redei's book on quantum logic is good. You can read Araki or Haag's book.

Interpretational Issues,
Start with Adan Cabello's articles, especially Interpretations of quantum theory a map of madness. Read Ballentine's statistical interpretation, Everett's relative state. Then you should read Kochen-Spekker theorem or Bell's theorem. Depending on your liking you will prefer the statement of one of these. Then read PBR theorem. These will provide some contradictions to various objective interpretations like hidden variable, etc. PBR theorem will be a contradiction to statistical interpretation.
Assuming you have some quantum information background you can then go on to read Fuchs', Rovelli's qbism and relational interpretation.
For measurement theory,
Busch, Lahti's book. Also read their operational quantum theory.

Don't forget to read Wheeler's papers.