In this document, we introduce XCSP3-core, a subset of XCSP3 that allows us to represent constraint satisfaction/optimization problems. The interest of XCSP3-core is multiple: (i) focusing on the most popular frameworks (CSP and COP) and constraints, (ii) facilitating the parsing process by means of dedicated XCSP3-core parsers written in Java and C++ (using callback functions), (iii) and defining a core format for comparisons (competitions) of constraint solvers.