This book is an exposition of what we know 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 also carefully explained. Physical concepts are established through mathematics, accurate numerical analysis and comparison of theory with experiments. Exercises are provided for students new to the subject. Researchers interested in topics ranging from transition to turbulence, hydrodynamic stability or combustion will find this book a useful resource, whether their background lies in engineering, physics, chemistry, biology, medicine or applied mathematics.