This books presents the fundamentals of nonlinear and mixed-integer optimization, and their applications in the important area of process synthesis in chemical engineering. The reader is acquainted with the basics of convex analysis and nonlinear optimization and is introduced to the elementary concepts of mixed-integer linear nonlinear optimization. Topics that are unique include the theory and methods for mixed-integer non-linear optimization, introduction to modeling issues in process synthesis, and optimization-based approaches in the synthesis of heat recovery systems, distillation-based systems, and reactor-based systems. This book fills a gap in available textbooks since there are no other books covering either the fundamentals or applications of nonlinear and mixed-integer optimization. It is designed keeping in mind that it can be used as a graduate textbook in one or two semester courses in nonlinear and mixed-integer optimization and applications in process synthesis, as well as a reference for any engineering student or researcher concerned with continuous and discrete nonlinear optimization issues in engineering design, process synthesis, process operations, applied mathematics and operations research, industrial management, and systems engineering.