This thesis shows the mathematical structure of the artwork ”Print Gallery” , made by the Dutch graphic artist Maurits Cornelis Escher (1898–1972). The explanation is based on the fact that lithography is viewed as an image on certain elliptic curves over the field of complex numbers and on the idea that picture is rotated until it is almost upside down and containing another copy of itself. More precisely, the image contains a copy of itself rotated at \(-157,625^{\circ}\) and reduced by factor 22.58. In Chapter 1 Escher’s method of his grid construction is presented. In Chapter 2, a generalized example explains complex transformations that are used to achieve Escher’s effect. Chapter 3 describes the theory of the modular group, the effect of Möbius transformations on the upper half-plane and the theory of complex torus. Then the Escher’s image on the complex torus is consider and the use of complex transformations from the 2nd chapter on the image, with the aim of obtaining a mapping which, with the help of a specially made software, enables to finish the image, as shown in Chapter 4.