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Let p : X → Y be a fibration between two projective manifolds.The Iitaka conjecture states that k(X)≥ k(Y)+k(X/Y),where k(X)is the Kodaira dimension of X and k(X/Y)is the Kodaira dimension of the general fiber.By using mainly the recent work of M.Paun and S.Takayama about the positivity of relatively canonical bundles,we give a proof of the Iitaka conjecture for algebraic fiber spaces over abelian varieties or over surfaces.This is joint work with M.Paun.