In the context of differential equations to integrate an equation means to solve it from initial conditions. Accordingly, an integrable system is a system of differential equations whose behavior is determined by initial conditions and which can be integrated from those initial conditions.
General dynamical systems
Hamiltonian systems and Liouville integrability
Action-angle variables
The Hamilton–Jacobi approach
Solitons and inverse spectral methods
Quantum integrable systems
Exactly solvable models
List of some well-known classical integrable systems