This is a sequel to my previous talk on the construction of a quiver from a triangulated bordered surface, which, as it turns out, provides a method to construct almost all the mutation-finite quivers, only with minor exceptions. To keep the talk self-contained, we shall first review the notions of quivers and their mutations, as well as the association of a quiver to a triangulated surface without a self-folded triangle. In particular, we recall how flips in triangulation correspond to quiver mutations. Then, we will move on to the discussion on the triangulations of surfaces with a self-folded triangle, and understand how this yields a more complete correspondence between flips and mutations. Finally, we shall see how quivers arising from triangulated surfaces play a major role in the classification of mutation-finite quivers.