This book deals with the study of new dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The book consists of four parts. Part I present a brief account of Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with an analog of Dold congruences for the Reidemeister and Nielsen numbers. Part IV explains how dynamical zeta functions give rise to Reidemeister torsion, a very important topological invariant which has useful applications in knots theory, quantum field theory and dynamical systems.