The subject matter of this book constitutes a merging of several directions of work in general model theory over the last 25 years. Three main lines can be distinguished: first, that initiated by Andrzej Mostowski on cardinality quantifiers; second, the work of Alfred Tarski, his colleagues and students on infinitary languages; and, finally, that stemming from the results of Per Lindstrom on generalized quantifiers and abstract characterizations of first-order logic.