Ludwig Wittgenstein is one of the most important and influential philosophers of the twentieth century, but he is also one of the least accessible. This volume provides a comprehensible guide to his work by a wide range of experts who are actively engaged in new work on Wittgenstein. The essays, which are both expository and original, address central themes in his philosophy of mind, language, logic, and mathematics and clarify the connections among the different stages in the development of his work.