Learnability theory is an attempt to illuminate the concept of learnability using a mathematical model of learning. Two models of learning of categorial grammars are examined here: the standard model, in which sentences presented to the learner are flat strings of words, and one in which sentences are presented in the form of functor-argument structures. The resulting two notions of learnability are logically independent, but have some indirect correlation. The first chapter presents the concept of learnability in relation to languages, and the second outlines the rudiments of learnability theory and some important results of research. Chapter 3 presents a general theorem concerning a certain property of language classes that guarantees learnability. Chapter 4 introduces classical categorial grammar, and chapter 5 lays out a basic theory of rigid grammars, a special class of categorial grammars of concern here. The next two chapters examine learnability from structures of various classes of categorial grammars, and chapter 8 looks at learnability from strings. Two variations of the formalism of classical categorial grammar are considered in chapter 9, and conclusions are drawn in the final chapter. Some learning algorithms are illustrated in the appendix. Contains 72 references. (MSE)