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We initiate a systematic analysis of moduli spaces of vacua of fourdimensional $\mathcal{N}=3$ SCFTs. Our analysis is based on the one hand on theproperties of $\mathcal{N}=3$ chiral rings --- which we review in detail andcontrast with chiral rings of theories with less supersymmetry --- and on theother hand on constraints coming from low-energy supersymmetry. This leads usto introduce a new type of geometric structure, which characterizes$\mathcal{N}=3$ SCFT moduli spaces, and that we call $triple\ special\K\"ahler$ (TSK). A rank-$n$ TSK moduli space has complex dimension $3n$, and issingular at complex co-dimension 3 subspaces where charged states becomemassless. The structure of singularities defines a stratification of the TSKspace in terms of lower-dimensional TSK manifolds.

On the moduli spaces of 4d $\mathcal{N} = 3$ SCFTs I: triple special K\"ahler structure