[en] We derive the nucleon-nucleon interaction based on the most general chiral effective pion-nucleon Lagrangian using the method of unitary transformations. For that, we develop a power counting scheme consistent with this projection formalism. In contrast to previous results obtained in old-fashioned time-ordered perturbation theory, the method employed leads to energy-independent potentials. We discuss in detail the similarities and differences to the existing chiral nucleon-nucleon potentials. We also show that to leading order in the power counting, the three-nucleon forces vanish lending credit to the result obtained by Weinberg using old-fashioned time-ordered perturbation theory. We employ the chiral nucleon-nucleon potential to study scattering and bound state problems in the two-nucleon system. At next-to-leading order, this potential is the sum of renormalized one-pion and two-pion exchange and contact interactions. At next-to-next-to-leading order, we have additional chiral two-pion exchange with low-energy constants determined from pion-nucleon scattering. Alternatively, we consider the delta-resonance as an explicit degree of freedom in the effective field theory. The nine parameters related to the contact interactions can be determined by a fit to the neutron-proton S- and P-waves and the mixing parameter ε₁ for laboratory energies below 100 MeV. The predicted phase shifts and mixing parameters for higher energies and higher angular momenta are mostly well described for energies below 300 MeV. The S-waves are described as precisely as in modern phenomenological potentials. We observe a good agreement with experimentally measured deuteron properties. We also discuss various charge symmetry and charge independence breaking effects in the ¹S₀ channel, in which the largest isospin violating effects are observed. (orig.)