I The Great Prize, the framework -- I.1 The iteration problem in 1915 -- I.2 The protagonists around 1917–1918 -- I.3 The war.- I.4 Iteration, a few definitions and notation -- I.5 Normal families -- I.6 Relation to functional equations -- II The Great Prize of Mathematical -- II.1 Year 1917 -- II.2 Year 1918 -- III The memoirs -- III.1 Julia’s memoir -- III.2 The (three) memoir(s) of Fatou -- III.3 Comments (in the first person) -- III.4 To summarise -- IV After Fatou and Julia -- IV.1 Stop -- IV.2 Hausdorff distance (1914) and dimension (1919) -- IV.3 Irregular points, J-points, O-points (1925–1927) -- IV.4 The centre problem (1927–1942).-IV.5 Holomorphic dynamics.-V On Pierre Fatou.-V.1 Childhood and youth of Fatou -- V.2 What do we know of Pierre Fatou? -- V.3 Continuation of Fatou’s career -- V.4 Fatou’s thesis -- V.5 Fatou as a mathematician.-V.6 Fatou as an astronomer -- V.7 Teaching and candidatures of Fatou -- V.8 Fatou and other mathematicians -- V.9 Death of Fatou -- VI A controversy in 1965 -- VI.1 The protagonists, from 1918 to 1965 -- VI.2 Relations between Julia and Montel, in the 1930’s -- VI.3 The third centenary of the Institut de France VI.4 -- As a conclusion: O for a biography of Gaston Julia -- References.-Index.

How did Pierre Fatou and Gaston Julia create what we now call Complex Dynamics, in the context of the early twentieth century and especially of the First World War? The book is based partly on new, unpublished sources.Who were Pierre Fatou, Gaston Julia, Paul Montel? New biographical information is given on the little known mathematician that was Pierre Fatou. How did the serious WW1 injury of Julia influence mathematical life in France? From the reviews of the French edition: "Audin’s book is indeed filled with marvelous biographical information and analysis, dealing not just with the men mentioned in the book’s title but a large number of other players, too … . the book under review addresses itself to scholars for whom the history of mathematics has a particular resonance and especially to mathematicians active, or even with merely an interest in, complex dynamics. … presents it all to the reader in a very appealing form." (Michael Berg, The Mathematical Association of America, October 2009).