The recoilless nuclear resonance absorption of gamma radiation (Mößbauer Effect) is applied in a number of ways, especially in the areas of solid state physics, magnetism, metallurgy, chemistry, biology, polymer physics, and medicine. To this day, thousands of papers are published annually by hundreds of laboratories; their headlines are compiled in a Data Index published annually. The paper deals with the basic principles of the effect, and with applications of interest especially in chemistry.