The last twenty years have witnessed a significant growth of interest in optimal factorial designs, under possible model uncertainty, via the minimum aberration and related criteria. This book gives, for the first time in book form, a comprehensive and up-to-date account of this modern theory. Factorial design plays a fundamental role in efficient and economic experimentation with multiple input variables, and is extremely popular in various fields of application, including engineering, agriculture, medicine and life sciences. Many major classes of designs are covered in the book. While maintaining a high level of mathematical rigor, it also provides extensive design tables for research and practical purposes. Apart from being useful to researchers and practitioners, the book can form the core of a graduate level course in experimental design. It can also be used for courses in combinatorial designs or combinatorial mathematics.