We present a new version of PyR@TE, a Python tool for the computation of renormalization group equations for general, non-supersymmetric gauge theories. Its new core relies on a recent paper by Poole & Thomsen (2019) to compute the β-functions. In this framework, gauge kinetic mixing is naturally implemented, and the Weyl consistency relations between gauge, quartic and Yukawa couplings are automatically satisfied. One of the main new features is the possibility for the user to compute the gauge coupling β-functions up to the three-loop order. Large parts of the PyR@TE code have been rewritten and improved, including the group theory module PyLie. As a result, the overall performance in terms of computation speed was drastically improved and the model file is more flexible and user-friendly. Program Title: PyR@TE 3 CPC Library link to program files:https://doi.org/10.17632/8h454kdd5n.2 Licensing provisions: Apache 2.0 Programming language: Python 3 Journal reference of previous version: PyR@TE 1, PyR@TE 2 2 Does the new version supersede the previous version?: Yes. Reasons for new version: The software was essentially rewritten and new functionalities were added. The performance in terms of computation speed was improved by a factor of 100 to 10000 compared to the previous version. The code now relies on Python 3 instead of the deprecated Python 2. Summary of revisions: The core of the software was rewritten, based on a new formalism. One of the major new features is the possibility of computing the 3-loop RGEs for gauge couplings. The structure and the syntax of the model file were enhanced. The output of the software was improved. Nature of problem : Computing the renormalization group equations for any renormalizable, 4-dimensional, non-supersymmetric quantum field theory. Solution method: Group theory, tensor algebra. References: 1 F. Lyonnet, I. Schienbein, F. Staub, A. Wingerter, PyR@TE: Renormalization group equations for general gauge theories 185 (3) 1130–1152. http://dx.doi.org/10.1016/j.cpc.2013.12.002. 2 F. Lyonnet, I. Schienbein, PyR@TE 2: A Python tool for computing RGEs at two-loop 213 181–196. http://dx.doi.org/10.1016/j.cpc.2016.12.003.