Selected Chapters in the Calculus of Variations These lecture notes describe the Aubry Mather Theory within the calculus of variations. The text consists of the translated original lectures of Jürgen Moser and a bibliographic appendix with comments on the current state of the art in this field of interest. Students will find a rapid introduction to the calculus of variations leading to modern dynamical systems theory. Differential geometric applications are discussed in particular billiards and minimal geodesics on the two dimensional torus. Many exercises and open questions make this book a valuable resource for both teaching and research