pyMOR is a software library for building model order reduction applications with the Python programming language. Implemented algorithms include reduced basis methods for parametric linear and non-linear problems, as well as system-theoretic methods such as balanced truncation or IRKA (Iterative Rational Krylov Algorithm). All algorithms in pyMOR are formulated in terms of abstract interfaces for seamless integration with external PDE (Partial Differential Equation) solver packages. Moreover, pure Python implementations of FEM (Finite Element Method) and FVM (Finite Volume Method) discretizations using the NumPy/SciPy scientific computing stack are provided for getting started quickly. For more information, visit