As the title of this monograph implies, our main goal is to provide and illustrate the use of functions (by way of M-files) within a MATLAB® computational environment to effect a variety of structural representations for proximity information assumed available on a set of objects. The structural representations that will be of interest have been discussed and developed primarily in the applied (behavioral science) statistical literature (e.g., in psychometrics and classification), although interest in these topics has now extended much more widely (for example, to bioinformatics and chemometrics). We subdivide the monograph into three main sections depending on the general class of representations being discussed. Part I develops linear and circular uni- and multidimensional scaling using the city-block metric as the major representational device; Part II is concerned with characterizations based on various graph-theoretic tree structures, specifically with those usually referred to as ultrametrics and additive trees; Part III uses representations defined solely by order properties, particularly to what are called (strongly) anti-Robinson forms. Irrespective of the part of the monograph being discussed, there will generally be two kinds of proximity information analyzed: one-mode and two-mode. One-mode proximity data are defined between the n objects from a single set, usually given in the form of a square (n x n) symmetric matrix with a zero main diagonal; two-mode proximity data are defined between the objects from two distinct sets containing, say, na and rib objects, respectively, and given in the form of a rectangular (na x rib) matrix. Also, there will generally be the flexibility to allow the fitting (additively) of multiple structures to either the given one- or two-mode proximity information.