The long-range transport of air pollutants and the reduction of air pollution to an acceptable level is an important environmental problem. The mathematical models by which this problem can be successfully studied are normally described by partial differential equations. The discretization in space leads to huge systems of ordinary differential equations containing up to several million equations that are to be handled during many time steps. This shows why the numerical treatment of these problems always causes difficulties, even if high-speed computers are available. Several problems connected with the computer treatment of air pollution models are discussed. While there are many excellent papers devoted to this subject, this is the first book where an attempt is made to study these problems systematically. This book may be useful for many specialists in air pollution modelling. Some topics are treated rather generally, therefore the book may also be used as a reference source by many scientists and engineers working with large mathematical tools.