Skew braces of size $p^{2}q$ I: abelian type

This is the first part of a series of two articles. In this paper we enumerate and classify the left braces of size $p^{2}q$ where $p$ and $q$ are distinct prime numbers by the classification of regular subgroups of the holomorph of the abelian groups of the same order. We also provide the formulas that define the constructed braces.