Design of cyber-physical systems today relies on executable models. Designers develop models, simulate them, find defects, and improve their designs before the system is built, thus greatly reducing the design costs. However, current model-based design methods lack support for model libraries (creating and exchanging models as "black boxes"), tool interoperability (allowing models to be co-simulated by multiple tools), and multi-view modeling (allowing to combine models that "live in different worlds", for instance, a control-logic model with an energy-consumption model). This project seeks to remedy this by developing a compositional modeling framework based on interfaces. Interfaces allow submodels to be treated as black boxes, exposing relevant information while hiding internal details. Success of the project will provide a solid theoretical foundation for compositionality in cyber-physical systems. Compositionality is a key property in system design, allowing to build systems in a scalable and modular manner. This project will enable the construction of model libraries, allowing the exchange of models developed by different teams, potentially coming from different disciplines and using different modeling languages and tools. Besides the considerable economic and societal impact of cyber-physical systems in general, the proposed project will have considerable impact on engineering and computer science education. Its focus on a rigorous and unified modeling theory will erode the boundaries between the currently separated cyber-physical system sub-disciplines that hamper competitiveness of our students. Finally, the project is strategically important for the competitiveness of the United States as it strengthens its presence in international standardization efforts for model exchange and co-simulation.