This book, first published in 2003, is an exposition of what we knew about the physics underlying the onset of instability in liquid sheets and jets. Wave motion and breakup phenomena subsequent to the onset of instability are carefully explained. Physical concepts are established through rigorous mathematics, accurate numerical analyses and comparison of theory with experiment. Exercises are provided for students, and these help familiarize the reader with the required mathematical tools. This book further provides a rational basis for designing equipment and processes involving the phenomena of sheet and jet breakup. Researchers interested in transition to turbulence, hydrodynamic stability or combustion will find this book a highly useful resource, whether their background lies in engineering, physics, chemistry, biology, medicine or applied mathematics.