This article presents the MAGI software package for the inference of dynamic systems. The focus of MAGI is on dynamics modeled by nonlinear ordinary differential equations with unknown parameters. While such models are widely used in science and engineering, the available experimental data for parameter estimation may be noisy and sparse. Furthermore, some system components may be entirely unobserved. MAGI solves this inference problem with the help of manifold-constrained Gaussian processes within a Bayesian statistical framework, whereas unobserved components have posed a significant challenge for existing software. We use several realistic examples to illustrate the functionality of MAGI. The user may choose to use the package in any of the R, MATLAB, and Python environments.

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