I will report on a joint work with S. Coughlan, R. Pardini and S. Rollenske. The investigation of (minimal) surfaces of general type with low invariants and their moduli spaces started with the work of Castelnuovo and Enriques and during the last decades of the $20$th century many authors continued studying these surfaces. Nowadays Gieseker's moduli space of canonical models of surfaces of general type with $K^2$ and $\chi$ fixed is known to admit a modular compactification, namely the KSBA moduli space, obtained considering stable surfaces. The structure of such moduli space is not completely known and studying stable surfaces with low invariants is a starting point to see concrete examples and studying its properties. The aim of this talk is to give a description of the he KSBA moduli space of stable surfaces with $K^2=1$ and $\chi=3$, showing different ways to construct boundary components. After an overview of the know components, I will focus on the case of $2$-Gorenstein surfaces, (with particular attention to the surfaces obtained by gluing two irreducible surfaces) and to the case of normal surfaces having rational singularities.