This is a welcome new edition of the author’s popular graduate textbook on the function theoretic aspects of several complex variables [first edition, Wiley (1982; Zbl 0471.32008)]. Besides updating the text and making minor emendations, the author has added some material. There is a new chapter about the inner function problem and the constructive methods that where used to solve it. Also, the concluding chapter has new sections that briefly treat complex analytic dynamics in two complex variables, the notion of finite type, and the work of Lempert on the Kobayashi metric.