The method of generating functions is extremely useful in enumeration problems. With the aid of generating functions we can discover a host of new identities, divisibility properties and asymptotical behavior 1 of our counting sequences. This chapter needs some knowledge from the reader’s side in analyis, especially differential and integral calculus, and some basics from differential equations. In a non-essential way, some matrix algebra will also be used. An excellent book which contains a detailed discussion of generating functions is [262] 2 .