The book has five chapters. Chapter 1 gives the basic knowledge needed to understand the contents of this book. Chapter 2 describes several interesting formulas related to harmonic numbers. In Chapter 3, the series problems involving several kinds of harmonics in the general terms are shown together with the solution to these problems can be found in mathematical references dealing with difficult problems. Chapter 4 presents the problem of multiple series involving several kinds of harmonics in general terms with solutions. Chapter 5 presents interesting challenges and open problems involving harmonic numbers in general terms.Since we have raised a number of interesting problems and various technical problems to solve them, this book will be a good reference not only for those specializing in mathematics, but also for those specializing in physics or other natural sciences.