As indigenous production declines, the European gas market is becoming increasingly dependent on imports. This poses energy security questions for a number of countries, particularly in the north-east of Europe. A suite of mathematical models of the European natural gas network has been borne from these concerns and has traditionally been used to assess supply disruption scenarios. The literature reveals that most existing European gas network models are insufficiently specified to analyse changes in supply and demand dynamics, appraise proposed infrastructure investments, and assess the impacts of supply disruption scenarios over a range of time horizons. Furthermore, those that are suited to these applications are typically proprietary and therefore publicly unavailable. This offers an opportunity to present a new model. The Gas Network Optimisation Model for Europe (GNOME) is a dynamic, highly granular mixed-integer linear optimisation model of the European natural gas network and its exogenous suppliers. GNOME represents demand and supply for all EU-27 Member States except Cyprus, Luxembourg, and Malta. The UK, Norway, Switzerland, Belarus, Ukraine, and Turkey are also included. Russia, the Southern Corridor suppliers, Qatar, North Africa, Nigeria, and the Americas are modelled as supply-only regions. GNOME satisfies gas demand in each country by generating a cost-minimal mix of indigenous gas production, pipeline flows, LNG imports, and storage use. If demand cannot be met using existing infrastructure, GNOME will generate a cost-optimal investment strategy of pipeline, LNG regasification, and gas storage capacity additions. The model solves on a monthly basis, from 2025 to 2040, in 5-year steps. The capabilities of GNOME are demonstrated by tasking it to analyse the impacts of a failure to complete the upcoming Nord Stream 2 pipeline between Russia and Germany. The complete formulation of GNOME including input files, equations, and source code is provided.