Over the last several decades, modern filter theory has been significantly embellished by many contributors. In Zverev’s [l] words “This search for useful theories has led to some of the most elegant mathematics to be found in the practical arts.” Excitement over this elegance is tainted by sophistication more suited for the filter mathematician than the engineer whose work is often less specialized. This book is directed to the engineer and not the mathematician. We do so in full reverence of the mathematicians who provided the tools to work with in the trenches.For completeness, a review of which predates WW II. more recent and some is of classic material is included, some Of course most of the material is 1original. It is at times a strange mixture, but always directed at the practical application of the art to today’s real-world problems. Chapters 1 through 5 cover fundamental concepts. Although this book emphasizes microwave filters, the first few chapters cover lumped element concepts more heavily than distributed elements. This is for two reasons. First, even at several gigahertz, lumped elements are useful when size is important, when stopband performance is critical and for MMIC processes. Second, much of the lumped element theory, with suitable modification, is applicable to distributed filter development. Many engineers now at the peak of their careers began with slide rules. Less than one floating point multiply per second is performed to about three digits of precision using a slide rule.