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Aurore is a free software application based on MATLAB scripts designed for the graphical analysis, inspection and simulation of neutron reflectivity data. Its architecture, combined with graphics and other advantages of the MATLAB environment, should allow continued development of this software and inclusion of new features and analysis methods. The development of the software was driven by the necessity for a non-commercial open-source application for the analysis of neutron reflectivity data. Aurore provides a robust and reliable method for evaluation of parameter uncertainty, a feature almost absent in similar software applications. In the present paper the main functionalities of the software are presented, together with a comprehensive description of the modeling approaches available at the moment. The code is released under a Creative Commons Attribution Non-Commercial License V2.0. The software application can be downloaded at http://aurorenr.sourceforge.net/.