[Truncated abstract] The field of pattern recognition aims to develop algorithms and computer programs that can learn patterns from data, where learning encompasses the problems of recognition, representation, classification and prediction. Syntactic pattern recognition recognises that patterns may be hierarchically structured. Formal language theory is an example of a syntactic approach, and is used extensively in computer languages and speech processing. However, the underlying structure of language and speech is strictly one-dimensional. The application of syntactic pattern recognition to the analysis of images requires an extension of formal language theory. Thus, this thesis extends and generalises formal language theory to apply to data that have possibly multi-dimensional underlying structure and also hierarchic structure . . . As in the case for curves, shapes are modelled as a sequence of local relationships between the curves, and these are estimated using a training sample. Syntactic square detection was extremely successful – detecting 100% of squares in images containing only a single square, and over 50% of the squares in images containing ten squares highly likely to be partially or severely occluded. The detection and classification of polygons was successful, despite a tendency for occluded squares and rectangles to be confused. The algorithm also peformed well on real images containing fish. The success of the syntactic approaches for detecting edges, detecting curves and detecting, classifying and counting occluded shapes is evidence of the potential of syntactic models.