A higher dimensional analogue of Kodaira's canonical bundle formula is obtained. As applications, we prove that the log-canonical ring of a klt pair with $\kappa \le 3$ is finitely generated, and that there exists an effectively computable natural number $M$ such that $|M K_X|$ induces the Iitaka fibering for every algebraic threefold $X$ with Kodaira dimension $\kappa=1$.