Three consequent concepts that build up the algorithm of the identification of modern landscapes on the Moon surface are suggested. They are anaglyphonosphere axiomatic and landscape concepts obtained with the use of the axiomatic method. The first concept depicts the geographic envelope of the Moon as an anaglyphonosphere layer (relief) that is a continuum (total environment). The latter becomes the research subject for both a geomorphologist and a landscape researcher. Continuity, dynamics, range (amplitude), and erosion potential determine anaglyphonosphere. Axiomatic concept means constructing the sole scheme (mathematically determined) of the search for the elementary surface units using the geometric interpretation of surface patterns of the Moon and its landscape interpretation. The landscape concept is based on the classical principles of the landscape theory and the axiomatic principles of the previous concept. The synthesis of concepts is implemented in the models of Moon landscapes of four scales: zero, linear, two-and three-dimensional. The paper offers the last two models of Davy Catena. Proposed concepts with appropriate correction can be used in parallel studies of the natural environment: geological, geomorphological, climatic, etc. The advantages of the axiomatic method consist in the objective approach to the division of the surface into specific units (the landscapes in our case). The proposed method of identifying and displaying the landscape complexes on the lunar surface can be a significant complement for the study and mapping of terrestrial planets, satellites of planet-giants, etc.