The book "Divergent Series, Summability and Resurgence III" by Eric Delabaere is the third volume of a specialized series that deals with the theory of divergent series and their applications in mathematics and theoretical physics. This volume pursues a dual approach: on one hand, it applies the resurgent methods introduced in Volume 1 to nonlinear problems, which necessitates the development of further properties of resurgence theory. On the other hand, it analyzes the fundamental example of the first Painlevé equation, advancing the resurgent analysis of singularities up to the so-called "bridge equation." This equation encapsulates all information about the nonlinear Stokes phenomenon at infinity of the first Painlevé equation. The book is aimed at students, mathematicians, and theoretical physicists interested in divergent power series and related problems.