Higher Gauge Structures and Invariant Action Principles

I present the systematic construction of gauge theories based on free differential and L-infinity algebras. This provides a consistent algebraic framework for constructing gauge-invariant theories whose field content is extended by higher-degree differential forms as gauge potentials. I derive explicit expressions for the corresponding extended Chern-Simons actions and the generalized anomaly terms that emerge from them. Possible applications to gravity and supergravity will also be discussed.