None of the current plethora of (meta-)modelling tools include a complete model of themselves. Such a model, a precise specification of the tool's syntax and semantics, allows for introspection and reflection. This enables features such as debugging. Without such a model, it is harder to decompose a tool into components for distribution, reason about efficiency, and reuse components of existing implementations. In this technical report, we present the foundations of the Modelverse, a self-describable environment for multi-paradigm modelling (supporting multi-formalism and multi-abstraction modelling and explicitly modelled processes). The foundations describe a class of Modelverse realizations, which satisfy our identified set of requirements. Conceptually, all information in the Modelverse is stored in a graph, and model management operations transform this graph. Parts of the graph also describes action constructs which, amongst others, can be used to define (linguistic) conformance relations, the basis for multi-layer multi-level modelling.