Drilling circulation systems in the oil and gas industry have advanced significantly in the last decade. The major changes resulted from the merging of air and gas drilling and underbalanced drilling with traditional liquid drilling systems. During the several years of teaching drilling engineering courses in both academic and industry, the authors realised the need for a book that covers modern drilling practices. The books that are currently available fill to provide adequate information about how engineering principles are applied to solving problems that are frequently encountered in drilling systems. This fact motivated the authors to write this book. This book is written primarily for well-drilling engineers and college students of both senior and graduate levels.