Transparent Intensional Logic (TIL) is the theory invented by Pavel Tichý, the Czech philosopher and logician who emigrated to New Zealand in 1970 and was a professor at the University of Otago at Dunedin up until his death in 1994.Over the last quarter of a century TIL has become a widely used system and been further developed both by the three authors and other Czech and Slovak logicians. Many articles presenting particular applications of TIL have been published, together with two books by Pavel Materna, in which he develops a new theory of concepts and conceptual systems on the basis of TIL. However, several papers have been published only in Czech or Slovak, many results have been superseded by new results that have only very recently been published, and various other results still await publication.Therefore, there is a pressing need for an updated systematic exposition of the foundations and applications of TIL. The proposed book will demonstrate how TIL lends itself to a broad range of applications. It comprises logical analysis of natural language (proposing solutions to many outstanding problems and puzzles), artificial-intelligence methods of knowledge representation, multi-agent systems in computer science, and philosophy of mathematics, among others. This book will cover all of the above, in particular new results concerning knowledge representation, attitude logic, incomplete meanings (anaphoric references), and philosophy of mathematics.