Using the Kaon-Spectrometer KaoS at the heavy-ion synchrotron SIS at the Gesellschaft f"ur Schwerionenforschung (GSI) in Darmstadt the production and emission of K+- and of K--mesons has been studied in Au+Au-reactions at a kinetic beam energy of 1.5 AGeV which is close to (K+) and far below (K-) the corresponding production thresholds of these particles in binary nucleon-nucleon collisions. The energy-differential and integrated production cross sections as well as the polar and azimuthal angle distributions have been measured as a function of the collision centrality. The K+- and the K--multiplicities show a stronger than proportional rise as a function of the number of nucleons participating in the reaction. This rise is similar for both types of particles as well as for the lighter collision system Ni+Ni. Hence the resulting K-/K+-ratio is constant as a function of the centrality and of the system size. This is explained by the coupling of the K--production to the K+-production via the “strangeness exchange”-reaction π Y → K- N since the hyperons Y are produced together with the K+ according to transport models. For all centralities the energy distributions of the K+-cross sections show a larger inverse slope parameter than those of the K--cross sections when fitted with a Maxwell-Boltzmann distribution. In addition the K+ show a forward-backward peaked emission pattern as a function of the polar angle for all collision centralities. For peripheral collisions the K- show this effect as well but less pronounced. The K--emission from central collisions is nearly isotropic. These observations are in agreement with the assumption of different emission times for K+ and for K-. The azimuthal angle distribution of the K+ shows a preferential emission perpendicular to the reaction plane which is explained by some transport-model caculations as the influence of a repulsive K+-Nucleon potential, whereas it is attributed by another calculation to the rescattering at the nucleons of the projectile fragments. For the first time, results on the dependence of the K--emission on the azimuthal angle are presented. The results presented emphasize the importance of the “strangeness exchange”-reaction at SIS-energies, on the one hand for the coupling of the K--production to the K+-production, on the other hand for the different emission behaviour, which is due to different emission times, caused by the K--absorption via this reaction.