The growth of the first ten layers of organic thin films on a smooth metallic substrate has been investigated in real-time using the model system PTCDA on Ag(111). The complex behaviour is comprehensively studied by electron microscopy, spectroscopy and diffraction in a combined PEEM/LEEM instrument revealing several new phenomena and yielding a consistent picture of this layer growth. PTCDA grows above room temperature in a Stranski-Krastanov mode, forming three-dimensional islands on a stable bi-layer, in competition with metastable 3rd and 4th layers. Around room temperature this growth mode changes into a quasi layer-by-layer growth, while at temperatures below about 250 K a Vollmer-Weber-like behaviour is observed. By means of laterally resolved soft X-ray absorption spectroscopy the orientation of all adsorbed molecules is found to be homogeneously flat lying on the surface, even during the growth process. The films grow epitaxially, showing long-range order with rotational domains. For the monolayer these domains could be directly analysed, showing an average size of several micrometers extending over substrate steps.