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In this chapter we collect axioms for quantum theory in one place and make some comments about them. However, this is very much a work in progress. In fact, this is one of the reasons that quantum theory remains so perplexing. And that is why the axiomatization is so important. Of course, on a day-to-day basis most scientists can take the appropriate Schrödinger equation as their starting point and work effectively with its quantum theory in order to understand new quantum systems and applications of quantum theory.