The objects studied are languages... which arise by generalization from first-order languages by allowing infinite conjunction and disjunction of fewer than [a fixed cardinal number of] formulas and simultaneous existential or universal quantification of fewer than [a fixed cardinal number of] variables. This is the first connected and detailed report of the important work done by the author, Tarski, Hanf and Scott on these languages. ... The monograph is carefully and lucidly written and should make this field of logic accessible to a wider circle of logicians.