These lectures describe the two main tools used for deconvolution in the context of radio aperture synthesis. The focus is on the basic issues, while other lectures at this school will deal with aspects closer to the actual practice of deconvolution. The practice is dominated by the descendants of a deceptively simple-looking , beautiful idea proposed by J. Högbom (A&A Suppl. 15 417 1974), which goes by the name of CLEAN. About the same time, another, rather different and perhaps less intuitive idea due to the physicist E.T. Jaynes was proposed by J.G. Ables (A&A Suppl 15 383 1974) for use in astronomy. This goes by the name of the Maximum Entropy Method, MEM for short. MEM took a long time to be accepted as a practical tool and even today is probably viewed as an exotic alternative to CLEAN. We will see, however, that there are situations in which it is likely to do better, and even be computationally faster. The goal of these lectures is to give enough background and motivation for new entrants to appreciate both CLEAN and MEM and go deeper into the literature.