In this work, an automated approach for 3D building roof modelling is presented. The method consists of two main parts, namely roof detection and 3D geometric modelling. For the detection, a combined approach of four methods achieved the best results, using slope-based DSM filtering as well as classification of multispectral images, elevation data and vertical LiDAR point density. In the evaluation, the combination of the four methods yields 94% correct detection at an omission error of 12%. Roof modelling is done by plane detection with RANSAC, followed by geometric refinement and merging of neighbouring segments to clean up oversegmentation. Walls are then detected and excluded, and the roof shapes are vectorised with the alpha-shape method. The resulting polygons are refined using 3D straight edges reconstructed by automatic straight edge extraction and matching, as well as 3D corner points constructed by intersection of the 3D edges. The results are quantitatively assessed by comparing to ground truth manually extracted from high-quality images, using several metrics for both the correctness and completeness of the roof polygons and for their geometric accuracy. The median value of correctness of the roof polygons is calculated as 96%, while the median value of completeness is 88%.