The point of departure of this book on Mathematical Linguistics is Lambek’s seminal paper ‘The Mathematics of Sentence Structure’ published in 1958 by the mathematician Joachim Lambek (1958) in which he presented the celebrated ‘Syntactic Calculus' L. We can say that Lambek formulated a system which could essentially capture the logic of string concatenation. From a linguistic point of view L turned out to be quite expressive and intuitive. But the logic of concatenation is a priori restricted in expressing mismatches between functors and dependents. In fact, it seems that a pervasive characteristic of natural languages is that functors/dependents are frequently not adjacent. This phenomenon can be named the problem of discontinuity of natural languages. This book has two goals: to give an extension of L (notated D) which is able to account for the problem of discontinuity and to maintain in D the good proof-theoretical and model-theoretical properties of L.