Higher-order interactions—those involving more than two elements—are fundamental to the complexity observed in biological, social, and technological systems. Traditional network models have primarily focused on pairwise interactions, connecting nodes through simple links. However, many real-world phenomena, such as group dynamics in social interactions or multifaceted biochemical reactions, cannot be adequately described by dyadic relationships alone. Understanding both the mechanisms (how the system's components are structured and interact) and the behaviors (the emergent properties and dynamics resulting from these interactions) is essential for a comprehensive analysis of complex systems. Integrating frameworks that model higher-order structures, like hypergraphs and simplicial complexes, with tools that analyze higher-order behaviors, such as information-theoretic methods, provides a more complete picture of these intricate systems.

In this course we aim to offer a cohesive overview of higher-order mechanisms and behaviors.