Magritte, a modern software library for 3D radiative transfer: I. Non-LTE atomic and molecular line modelling. Radiative transfer is a key component in almost all astrophysical and cosmological simulations. We present Magritte: a modern open-source software library for 3D radiative transfer. It uses a deterministic ray-tracer and formal solver, i.e. it computes the radiation field by tracing rays through the model and solving the radiative transfer equation in its second-order form along a fixed set of rays originating from each point. Magritte can handle structured and unstructured input meshes, as well as smoothed-particle hydrodynamics (SPH) particle data. In this first paper, we describe the numerical implementation, semi-analytic tests and cross-code benchmarks for the non-LTE line radiative transfer module of Magritte. This module uses the radiative transfer solver to self-consistently determine the populations of the quantised energy levels of atoms and molecules using an accelerated Lambda iteration (ALI) scheme. We compare Magritte with the established radiative transfer solvers Ratran (1D) and Lime (3D) on the van Zadelhoff benchmark and present a first application to a simple Keplerian disc model. Comparing with Lime, we conclude that Magritte produces more accurate and more precise results, especially at high optical depth, and that it is faster.

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