The monograph is the result of many years of research on syllogistic theories in terms of symbolic logic. A detailed classification of syllogistic systems is given depending on the expressive capabilities of their languages and the conditions of the truth of categorical statements accepted in them. A formal reconstruction of a number of syllogistics existing in the history of logic is being carried out - Aristotle syllogistics, L. Carroll, B. Bolzano, J. Venna, N. A. Vasilieva, as well as traditional and fundamental syllogistics. Metatheoretical relationships are established between various systems of syllogistics, as well as between syllogistics and modern logical theories. For several systems of syllogistics, adequate intensification semantics are offered. For the first time, the problem of completeness of a set of logical constants in the syllogistic theory is posed and investigated.