The Moon displays weak magnetic fields resulting from areas of the lunar crust that are remanently magnetised. The origins of the magnetic fields that produced this remanent magnetisation are still under discussion, and theories include among several, an ancient lunar dynamo, or processes occurring on the Moon as a result of impacts. Lunar crustal fields have been mapped globally by the Magnetometer (MAG) and Electron Reflectometer (ER) on the satellite Lunar Prospector, providing vector magnetic field measurements at an average altitude of 30 km, and estimates of the total surface field. This thesis presents global and regional models of the magnitude and direction of lunar magnetisation within a layer, produced from both the MAG and ER data independently and jointly using several inversion methods. The inverse modelling techniques are based on those developed for terrestrial and Martian data sets, employing equivalent source dipoles as basis functions, and Green’s functions relating a magnetic field observation to a spatially continuous magnetisation distribution. A unique magnetisation solution is selected having the smallest rootmean- square (RMS) magnetisation for a given fit to the data, controlled by a damping parameter. The non-uniqueness in magnetisation distributions and the determination of source parameters is discussed with the use of forward models to assist the interpretation of the crustal magnetisation models. Suites of magnetisation models for layers with thicknesses between 10 and 50 km, and with different dipole depths, are able to reproduce both the ER and MAG data well. Inverse models utilising the scalar ER data have been developed successfully, resulting in a joint inversion of the ER and MAG data for one of the strongest magnetic anomalies on the Moon, Reiner Gamma. The largest concentrations of strongly magnetised crust are, like the crustal fields themselves, located antipodal to the youngest large impact basins, and in some isolated areas associated with the strongest crustal fields. The magnetisation distributions show robust magnitudes with different data sets and modelling techniques showing the extent of magnetised sources, but can not be used to infer the direction of the magnetising fields. Average magnetisation values in magnetised regions of 30-40 mA/m are similar to the measured magnetisations of the Apollo samples and significantly weaker than crustal magnetisations for Mars and the Earth. A global preference for a 30 km thick magnetised layer suggests that a dynamo field may be more consistent with these magnetisation models. The magnetisation models in this thesis are the first global magnetisation models for the Moon, and the first to combine the vector MAG and the scalar ER data. These magnetisation models can be used to predict the crustal contribution to the lunar magnetic field environment at a particular location, and in the absence of reliable sample returns, provide valuable information on the magnitude of lunar crustal magnetisation.