This book is a record of a seminar on mathematical logic Kurt Gödel and Hans Hahn held in Vienna in 1931-32. The seminar proceedings, given in English translation, are a unique witness of the state of research in logic and foundations of mathematics right after Gödel had published his celebrated incompleteness theorems. The seminars explain Gödels results in logic in detail, in contrast to his publications of the time that often were quite laconic and extremely short. This book also contains Gödels trial lecture on intuitionistic logic held in Vienna in 1933. The manuscript, recently found among the Gödel papers kept in Princeton, is preserved in Gödels forgotten German shorthand and published here in an English translation.     The book also adds an important aspect to the intellectual history of Vienna, as both Gödel and Hahn were members of the Vienna Circle group of philosophers and scientists.