  We present the state-of-the-art single-zone nuclear reaction network WinNet
that is capable of calculating the nucleosynthetic yields of a large variety of
astrophysical environments and conditions. This ranges from the calculation of
the primordial nucleosynthesis, where only a few nuclei are considered, to the
ejecta of neutron star mergers with several thousands of involved nuclei. Here
we describe the underlying physics and implementation details of the reaction
network. We additionally present the numerical implementation of two different
integration methods, the implicit Euler method and Gears method along with
their advantages and disadvantages. We furthermore describe basic example cases
of thermodynamic conditions that we provide together with the network and
demonstrate the reliability of the code by using simple test cases. With this
publication, WinNet is publicly available and open source at GitHub and Zenodo.
