This volume gives an up-to-date review of the subject Integration in Finite Terms. The book collects four significant textstogether with an extensive bibliography and commentaries discussing these worksand their impact. These texts,either out of print or never publishedbefore, are fundamental to the subject of the book. Applications in combinatorics and physics have aroused a renewed interest in this well-developed area devoted to finding solutions of differential equations and, in particular, antiderivatives, expressible in terms of classes of elementary and special functions.