Casimir forces

The present notes are organized as the lectures given at the Les Houches Summer School "Quantum Optics and Nanophotonics" in August 2013. The first section contains an introduction and a description of the current state-of-the-art for Casimir force measurements and their comparison with theory. The second and third sections are a pedagogical presentation of the main features of the theory of Casimir forces for 1-dimensional model systems and for mirrors in 3-dimensional space.