The chemical process industry faces serious problems in regard to new materials and efficient methods of production due to increasing costs of energy, stringent environmental regulations and global competition. A clear understanding of the processes is required in order to solve these problems. One way is through the crisp modelling method; another is through an optimal operation of the process to improve profitability and efficiency. The book is divided in two parts. The first part discusses the methods of modelling chemical engineering processes through well-known mathematical methods involving numerical calculations. This includes the recent concepts of Fuzzy logic and neural nets. The second part describes the efficient optimization methods, which can be effectively applied in many chemical processes. This involves methods of search for extrema as well as optimization, with and without constraint relations. Most books on nonlinear programming are theoretical, and the exact procedures of computation are often obscure. But in this book, a number of problems have been worked out. In addition to this, computer programs are included for almost all the topics. Due to the intricacy of optimization programs, the flow charts and the program in clear BASIC language have been provided so that the reader can understand the mathematical methods. The book will be useful for students and practising engineers in the field of chemical engineering, biotechnology, environmental engineering, and applied mathematics.