  In this paper we provide the basic setup for a project, initiated by Felix
Rehren, aiming at classifying all $2$-generated primitive axial agebras of
Monster type $(\alpha, \beta)$. We first revise Rehren's construction of an
initial object in the cathegory of primitive $n$-generated axial algebras
giving a formal one, filling some gaps and, though correcting some
inaccuracies, confirm Rehren's results. Then we focus on $2$-generated algebras
which naturally part into three cases: the two critical cases $\alpha=2\beta$
and $\alpha=4\beta$, and the generic case (i.e. all the rest). About these
cases, which will be dealt in detail in subsequent papers, we give bounds on
the dimensions (the generic case already treated by Rehen) and classify all
2-generated primitive axial algebras of Monster type $(\alpha, \beta)$ over
$\mathbb Q(\alpha, \beta)$ for $\alpha$ and $\beta$ algebraically independent
indeterminates over $\mathbb Q$. Finally we restrict to the $2$-generated
Majorana algebras (i.e. when $\alpha=\frac{1}{4}$ and $\beta=\frac{1}{32}$),
showing that these fall precisely into the nine isomorphism types of the
Norton-Sakuma algebras.
