In this paper, the focus is on low-level processing of SAR (Synthetic Aperture Radar) images, and the eventual goal is automatic classification employing various techniques based on Mathematical Morphology (MM). SAR images are characterized by considerable "speckle" noise, which gives rise to serious problems in early processing (filtering, edge detection). In order to overcome these problems, we have used the MM approach, in particular, operators for filtering such images to reduce "speckle" noise and to enhance straight lines, typical for man-made objects. Edges are detected and thinned to obtain as many continuous and closed contours as possible. Edge-based segmentation is then performed, and various features are obtained for each region. Moreover, we use and discuss MM tools also to compute the fractal dimension around each pixel with an adaptive technique. Finally, the resulting information is merged to achieve the correct splitting of an image into significant regions, each described by an appropriate set of features (shape, texture, skeleton, linear edges by the Hough transform, etc.), which are employed in the next classification step. Experimental results have been obtained by analyzing SAR images of a ground area in Algeria; they are shown and discussed in the paper.