From his return to Cambridge in 1929 to his death in 1951, Ludwig Wittgenstein, who published only one work in his lifetime, influenced philosophy almost exclusively through teaching and discussion. These lecture notes, therefore, are an important record of the development of Wittgenstein's thought; they indicate the interests he maintained in his later years and signal what he considered the salient features of his thinking. Further, the notes from an enlightening addition to his posthumously published writings. P. T. Geach, A. C. Jackson, and K. J. Shah kept meticulous notes from the last formal course that Wittgenstein taught at Cambridge. In order to reconstruct as accurately as possible the words of Wittgenstein, this volume compiles all three sets of notes with no attempt to conflate or edit them beyond rendering them into lucid English. Topics covered by the notes in this volume include the private language argument, the grammar of sensation statements, certainty and experimentation in psychology, and, in general, the same set of concerns as are to be found in his Last Writings and Remarks on the Philosophy of Psychology. The source material provided in these lecture notes is vital to Wittgenstein scholarship.