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PyMC3 (also goes by PyMC; it is the third version) is a Python library for modeling using Bayesian methods. It implements Markov chain Monte Carlo (MCMC), offering a number of algorithms, including the Metropolis algorithm, and newer algorithms such as No-U-Turn Sampler (NUTS).
PyMC3 is build on a more general Python library for such mathematical modeling, Theano, which, in turn is built on a Python library for numerical programming, NumPy. Theano's maintainers announced in 2017 that they would cease development and maintenance, leading to questions how to deal with that fact.