This book investigates the learnability of various classes of classical categorial grammars within the Gold paradigm of identification in the limit from positive data. Learning from structure and learning from flat strings are considered. The class of k-valued grammars, for k = 1,2,3,..., is shown to be learnable both from structures and from strings, while the class of least-valued grammars and the class of least-cardinality grammars are shown to be learnable from structures. In proving these learnable results, crucial use is made of a theorem on the concept known as finite elasticity. The learning algorithms used in this work build on Buszkowski and Penn's algorithm for finding categorial grammars from input consisting of functor-argument structures.