The first part of this lecture will be an introduction to the linear elastic fracture mechanics of brittle solids. In particular, we will focus on the emergence of a mechanical singularity and the dynamics of propagative ruptures. In the second part, we will see that frictional motion is a fracture process. Sliding between two solids occurs once the solid contacts are broken via the propagation of a brittle shear crack. We will show that fracture mechanics is a powerful tool to characterize the frictional properties of a solid interface, but not only. We willshow that friction provides a versatile platform for studying fracture dynamics and mechanical singularities: propagation and arrest criteria, equation of motion.