The systems biology markup language (SBML) permits to represent biological models mixing reaction networks, algebraic equations, differential equations, and events. Its main objective is to exchange biological models between various tools for simulation and analysis. Such tools are, for example, Copasi, BioCham, CellDesigner, as well as more general-purpose languages such as Julia. While an XML schema formally defines the concrete syntax of SBML, there is no formal semantics. This makes it often difficult to understand the models and to design and implement correct and general interfaces from and to SBML, i.e., to use SBML as an exchange formalism for systems biology. In the present paper, we propose Core SBML, a novel language covering a large subset of SBML with clear formal semantics. Besides giving a formal definition, we define an XML syntax for Core SBML by an XML schema. We then present a compiler of a large fragment of SBML to Core SBML. We also distinguish a fragment of Core SBML with a provably correct compiler to BioCham.