Providing an elementary introduction to branching random walks the main focus of these lecture
notes is on the asymptotic properties of one-dimensional discrete-time supercritical branching
random walks and in particular on extreme positions in each generation as well as the
evolution of these positions over time. Starting with the simple case of Galton-Watson trees
the text primarily concentrates on exploiting in various contexts the spinal structure of
branching random walks. The notes end with some applications to biased random walks on trees.
