We present the final analysis of the European Large Area Infrared Space Observatory (ISO) Survey (ELAIS) 15-μm observations, carried out with the ISO Camera (ISOCAM) instrument on board the ISO. The data-reduction method, known as the Lari Method, is based on a mathematical model of the behaviour of the detector and was specifically designed for the detection of faint sources in ISOCAM/ISO Photopolarimeter (ISOPHOT) data. The method is fully interactive and leads to very reliable and complete source lists. The resulting catalogue includes 1923 sources detected with signal-to-noise ratio of >5 in the 0.5-100mJy flux range and over an area of 10.85deg2 split into four fields, making it the largest non-serendipitous extragalactic source catalogue obtained to date from the ISO data. This paper presents the concepts underlying the data-reduction method together with its latest enhancements. The data-reduction process, the production and basic properties of the resulting catalogue are discussed. The catalogue quality is assessed by means of detailed simulations, optical identifications and comparison with previous analyses.