Accreting NS in their wide range of appearances are an important class of X-ray sources. They have been discussed mainly from an observational point of view. Several issues could not be covered within this chapter. For instance, NS in binaries are an important source of information on stellar evolution, of the evolution of Globular Clusters and the Galaxies in which they are found as a whole. There are for instance clear differences in the types of accreting NS binaries between our galaxy and the SMC and LMC, the low metallicity of which is thought to be responsible for the existence of exceptionally bright X-ray binaries. Among the known accreting NS systems, there are several exotic systems, like Aql X1 (showing both NS and BH behavior) or Cyg X-3 (which may not contain a NS but a BH), or systems with extremely rich and complex sets of information (and corresponding lack of physical understanding), like the Z- and Atoll-sources, the Bursting Pulsar, Her X-1 or others. Finally, there are many features - spectral as well as timing - which are found in a quite similar way in NS and in black holes, implying that the existence or not of a solid surface and a stellar magnetic field may not be so important. Likewise, the contributions of the research on accreting neutron stars to the determination of the most fundamental physical parameters of neutron stars, the mass, and radius, leading to constraints for the equation of state (EOS), as well as observations with relevance to general relativity effects in the immediate vicinity of the compact objects, are not discussed here. These aspects are discussed in the chapter 14 from the point of view of single neutron stars.

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