Gear mesh stiffness (GMS) is a critical parameter in modelling gearbox vibration response using lumped mass methods. Existing GMS models in the literature are often fragmented, limiting their application to broader condition-based maintenance strategies. This chapter introduces a generalised spur GMS model based on the potential energy method, which can integrate multiple fault types within a unified framework. The framework facilitates the computation of time-varying stiffness, incorporating bending, shear, axial, Hertzian, and fillet foundation effects, ensuring a physically consistent stiffness estimation. This is the first gear mesh stiffness model that simultaneously models multiple damage types within a single unified framework, which is advantageous for the gear condition-based maintenance community. This work represents the first of two parts. This first part is concerned with generalised stiffness modelling, with the second part addressing fault modelling. In addition to a rigorous mathematical description, the proposed methodology is implemented in an open-source Python package ( https://github.com/LukevanEyk/Gearbox-Simulator ), which allows users to input spur gear parameters, introduce faults, and analyse the resulting stiffness variations. By providing an accessible and computationally efficient approach, this framework supports academic research and industrial applications in gearbox diagnostics, condition monitoring, and predictive maintenance.