2-generated axial algebras of Monster type

We provide the basic setup for the project, initiated by Felix Rehren, aiming at classifying all 2-generated axial algebras of Monster type $(α,β)$ over a field $\mathbb F$. Using this, we first show that every such algebra has dimension at most 8, except for the case $(α,β)=(2,\tfrac{1}{2})$, where