What we will discuss in this book is their application in the summation of series together with interesting formulas related to harmonic numbers. Harmonic numbers have been attracted the gaze of a large mathematicians for it’s peculiar form and widely used in scientific and technical calculations. The results of the limits of sequences, infinite series and infinite products containing the harmonic number are very related with important mathematical constants like pi, Napier and Euler constants and special functions like Gamma and Riemann zeta functions. We have solved many series problems related to harmonic numbers through long-term studies, and we are going to introduce the results together with the results already presented in this book. We give solutions together with the problems in this book. We handle with fairly difficult problems and moreover open problems, and use important technologies like admirable limit and integral skills.