  In this paper we begin mapping out the space of rank-2 $\mathcal{N}=2$
superconformal field theories (SCFTs) in four dimensions. This represents an
ideal set of theories which can be potentially classified using purely quantum
field-theoretic tools, thus providing a precious case study to probe the
completeness of the current understanding of SCFTs, primarily derived from
string theory constructions. Here, we collect and systematize a large amount of
field theoretic data characterizing each theory. We also provide a detailed
description of each case and determine the theories' Coulomb, Higgs and Mixed
branch stratification. The theories naturally organize themselves into series
connected by RG flows but which have gaps suggesting that our current
understanding is not complete.
