<p>The main purpose of this work is to illustrate a methodology for mapping (identification and delineation) mounds and mountains on the lunar surface. In doing so, a precise meaning is given to positive relief in relation to a local base level which is specific to each mapped feature. The procedure is useful for mapping very shallow volcanic domes and cones, shallow wrinkle ridges and any other positive relief as shown in different test sites. The mapping of lunar mountains has allowed their sizes to be determined and compared with mountains on Earth which are defined using the same methodology. This paper reveals which is the mightiest mountain on the Moon and, by comparison to two emblematic Earth mountains (Mount Everest and Mount Kilimanjaro), it is shown that lunar mountains are mightier than Earth mountains despite the fact that they are more rounded and do not have the steep slopes of mountains on Earth. When comparing their slopes, the mean slopes inside circles of 3&#xa0;km radius around the summits are, respectively, 39º, 26º and 12º for Mount Everest, Mount Kilimanjaro and the mightiest lunar mountain. It is also shown that significant mountains on the Moon, in the form of volcanic cones, crater central peaks and mighty mountains, have the form of a three-sided pyramid. Given the DEM spatial resolution, the procedure is able to map any mound, which is illustrated by identifying very shallow volcanic domes and volcanic cones. Central crater peaks are also interesting mountains of medium altitude that may reach several thousand metres. The identification and delineation of mountains on the Moon is illustrated by using the LOLA digital elevation model but the methodology is completely general and the only limitation is the spatial resolution of the digital elevation model used to define the scale of the positive reliefs that can be identified and delineated.</p>