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This memoir begins a program to classify a large subclass of the class of simple saturated 2-fusion systems of component type. Such a classification would be of

A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and

Let p p be a prime and S S a finite p p-group. A p p-fusion system on S S is a category whose objects are the subgroups of S and whose morphisms are certain inj

These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.