Three great mathematicians dominate the history of lunar theory in the middle of the 18th century: Leonhard Euler, Alexis Clairaut, and Jean le Rond d'Alembert. Each of them made a lasting contribution to the theory of celestial mechanics and their results had a broader impact than on lunar theory alone. But the then most accurate tables of lunar motion were those of Tobias Mayer: not because he was better at solving the differential equations of motion, but because he was eager to handle large and conflicting data sets in what could nowadays be called a statistical way. He was a true pioneer in the `combination of observations', i.e., the handling of observational data in order to infer from them certain quantitative aspects of the physical reality. His tables of the moon's motion accomplished a break-through because they were accurate enough to make possible the determination of geographical longitude at sea, by the so-called method of lunar distances. / / The goal of the present study is to investigate the development of Tobias Mayer's lunar theory and tables. A major point concerns the causes of the accuracy of these tables: on several occasions, Mayer had announced that this was a result of the adjustment of the theory to observations. However, he did not report his procedures in full, neither in publications nor in extant letters, and until now it remained unknown how he managed to fit a model involving tens of parameters to a corpus of over a hundred observations. / / The relation between Mayer's tables and his theory is complicated and oblique. It was not, principally, the theory as published in his `Theoria Lunae juxta Systema Newtonianum' that he adjusted to observations. This has not been remarked before. Besides, most of the researchers in the history of celestial mechanics have skipped Mayer's lunar theory on the assumption that it is a straightforward derivative of Euler's. This assumption is no longer tenable after Euler's and Mayer's theories are compared, as I do in this thesis. / / What finally emerges (mostly of Mayer's unpublished manuscripts), is a drastically changed view of the origins of Tobias Mayer's lunar tables and lunar theory, of their interrelationship, and of their relations to the lunar theories of Euler, Clairaut, and (surprisingly!) Newton. I also present new insights into Mayer's dealing with random observational errors and related statistical concepts.