The small world networks considered in this chapter were originally designed to provide examples of networks whose clustering coefficient is not small (as is the case in locally tree-like networks), but in which shortest path lengths grow only logarithmically with the number of vertices if the expected degree of a typical vertex remains bounded (unlike what happens in random geometric graphs). These small world networks can be thought of as interpolating between the Bernoulli random graph and random geometric graphs, by superimposing one upon the other, thus reducing the shortest path lengths without greatly reducing the clustering coefficient. In a limiting version, in which random shortcuts are superimposed on a circle, it is shown that shortest path lengths between randomly chosen points of the circle are divided by a quantity roughly equal to the reciprocal of the number of shortcuts.