  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.
