This paper proposes a formalism to define chaos in both quantum and classical systems using adiabatic transformations. The complexity of adiabatic transformations that preserve classical time-averaged trajectories (quantum eigenstates) in response to Hamiltonian deformations is used as a measure of chaos. This complexity is quantified by the fidelity susceptibility. The paper shows that this measure can distinguish integrable, chaotic but non-thermalizing, and ergodic regimes. It applies the fidelity susceptibility to a model of two coupled spins and demonstrates that it successfully predicts the universal onset of chaos, both for finite spin S and in the classical limit S → ∞. The paper also shows that finite S effects are anomalously large close to integrability. The fidelity susceptibility is shown to characterize the complexity of special canonical transformations that leave invariant stationary probability distributions, which are direct analogues of quantum eigenstates. The paper illustrates how the fidelity susceptibility can be used to probe and define chaos in both quantum and classical systems, and shows that it is a universal probe of chaos, integrability, and ergodicity. The paper also shows that the fidelity susceptibility can be used to analyze the thermodynamic limit of quantum systems and that it is complementary to the high frequency spectral data encoded in the short-time behavior of operators. The paper concludes that the fidelity susceptibility is a powerful tool for studying chaos in both quantum and classical systems.This paper proposes a formalism to define chaos in both quantum and classical systems using adiabatic transformations. The complexity of adiabatic transformations that preserve classical time-averaged trajectories (quantum eigenstates) in response to Hamiltonian deformations is used as a measure of chaos. This complexity is quantified by the fidelity susceptibility. The paper shows that this measure can distinguish integrable, chaotic but non-thermalizing, and ergodic regimes. It applies the fidelity susceptibility to a model of two coupled spins and demonstrates that it successfully predicts the universal onset of chaos, both for finite spin S and in the classical limit S → ∞. The paper also shows that finite S effects are anomalously large close to integrability. The fidelity susceptibility is shown to characterize the complexity of special canonical transformations that leave invariant stationary probability distributions, which are direct analogues of quantum eigenstates. The paper illustrates how the fidelity susceptibility can be used to probe and define chaos in both quantum and classical systems, and shows that it is a universal probe of chaos, integrability, and ergodicity. The paper also shows that the fidelity susceptibility can be used to analyze the thermodynamic limit of quantum systems and that it is complementary to the high frequency spectral data encoded in the short-time behavior of operators. The paper concludes that the fidelity susceptibility is a powerful tool for studying chaos in both quantum and classical systems.