Preface.- Prologue: inside the energy walls of our cradle.- Gravity at small distances.- New fundamental forces of Nature?.- The graviphoton and the dilaton.- Chamaleons and fat gravitons.- New dimensions of space?.- The compact scenario.- The Kaluza-Klein towers and the radion.- A spontaneous compactification.- The brane-world scenario.- The geometric confinement of gravity.- Gravity at large distances.- Extra dimensions strike back.- A new form of dark energy?.- The cosmic quintessence.- The fluctuations of the vacuum energy.- Space, time and space-time.- Maybe the past can change?.- Time and memory.- Time: an intrinsic property of all bodies?.- Maybe space-time is not unique?.- Relative singularities.- Strings and fundamental interactions.- How to quantize extended objects.- Supersymmetry and higher-dimensional spaces.- The five superstrings.- Type IIA and type IIB superstrings.- Type I superstrings.- The two heterotic superstrings.- Conformal invariance and equations of motion.-The dilaton and the topological expansion.- A new symmetry: duality.- Winding strings and large dimensions.- The very early past of our Universe.- String cosmology.- Brane cosmology.- The ekpyrotic scenario.- Brane-antibrane inflation.- Signals from epochs before the Big Bang?.- The cosmic background of relic gravitons.- Conclusion.- References.- Index.