"Compressor Instability with Integral Methods" is a book, to bring together the quick integral approaches and advances in the field for the prediction of stall and surge problem in compressor. This book is useful for people involved in the flow analysis, design and testing of rotating machinery. For students, it can be used as a specialized topic of senior undergraduate or graduate study. The book can also be served as a self-study material to those who keen to acquire this knowledge. In brief, this book focuses on the numerical/computational analysis for the effect of distorted inlet flow propagation on the rotating stall and surge in axial compressors. It gains insight into the basic phenomena controlling these flow instabilities, and reveals the influence of inlet parameters on rotating stall and surge. The book starts from the confirmation and application of Kim et al's integral method and then follows by a development to this method through the proposing and applying a critical distortion line. This line is applied successfully on the stall prediction of in-flight compressor due to flamming of refueling leakage near inlet, a typical real and interesting example of compressor stall and surge operation. Further, after a parametric study on the integral method and the distorted flow field of compressor using Taguchi method, a novel integral method is formulated using more appropriate and practical airfoil characteristics, with a less assumptions needed for derivation. Finally, as an extended work, the famous Greitzer's instability flow model, the well-known B-parameter model applied for analyzing the stall and surge characteristics, is studied parametrically using Taguchi method.