Nutils is a Free and Open Source Python programming library for Finite Element Method computations, developed by Evalf Computing and distributed under the permissive MIT license. Key features are a readable, math centric syntax, an object oriented design, strict separation of topology and geometry, and high level function manipulations with support for automatic differentiation. Nutils provides the tools required to construct a typical simulation workflow in just a few lines of Python code, while at the same time leaving full flexibility to build novel workflows or interact with third party tools. With native support for Isogeometric Analysis (IGA), the Finite Cell method (FCM), multi-physics, mixed methods, and hierarchical refinement, Nutils is at the forefront of numerical discretization science. Efficient under-the-hood vectorization and built-in parallellisation provide for an effortless transition from academic research projects to full scale, real world applications.