 AQFT then imposes a whole list of axioms on the abstract algebraic structure, namely relativistic axioms (in particular locality and covariance), general physical assumptions (e.g. the spectrum condition), and finally some technical assumptions concerning the mathematical formulation. The principle of (Einstein) causality is the main relativistic ingredient of AQFT: All observables of a local algebra connected with a space-time region \(\mathcal{O}\) are required to commute with all observables of another algebra which is associated with a space-time region \(\mathcal{O}'\) that is space-like separated from \(\mathcal{O}\). As a reformulation of QFT, AQFT is expected to reproduce the main features of QFT, like the existence of antiparticles, internal quantum numbers, the relation of spin and statistics, etc. That this aim could not be achieved on a purely axiomatic basis is partly due to the fact that the connection between the respective key concepts of AQFT and QFT, i.e., algebras of observables and quantum fields, is not sufficiently clear. One main link are superselection rules, which put restrictions on the set of all observables and allow for classification schemes in terms of permanent or essential properties.