While Koopman operator linearization has brought many advances for prediction, control, and verification of dynamical systems, its main disadvantage is that the quality of the resulting model heavily depends on the correct tuning of hyper-parameters such as the number of observables. Our AutoKoopman toolbox is a Python package that automates learning accurate models in a Koopman linearized representation with low effort, offering several tuning strategies to optimize the hyper-parameters associated with the Koopman operator techniques automatically. AutoKoopman supports discrete as well as continuous-time models and implements all major types of observables, which are polynomials, random Fourier features, and neural networks. As we demonstrate on several benchmarks, our toolbox is able to automatically identify very accurate dynamic models for symbolic, black-box, as well as real systems.