Hamiltonian Theory: Dynamics

This chapter focuses on the status of the implementation of the dynamics in the canonical version of loop quantum gravity (LQG). Concretely, this means to provide a mathematical meaning of the quantum Einstein equations, sometimes called Wheeler-DeWitt equations, to give a physical interpretation and Hilbert space structure to its solutions, and to construct a representation of the algebra of observables including a physical Hamiltonian. This is a structural overview intentionally skipping technical details.