The multi-transition solutions mentioned in lectures 1-2 are generally obtained by what may be called variational gluing arguments. Minima of a functional are in a sense glued together to get new critical points and new solutions of the associated Euler equation. In other settings one deals with mountain pass critical points of a functional rather than minima. In this lecture, we will discuss these matters and also show how to construct hybrid solutions by gluing minimizers and mountain pass solutions.