This Chapter presents a summary, with detailed references, of the work of James Damon (1945–2022) whose untimely death deprived the mathematical community of a major figure and, equally, of an exceptionally kind and supportive friend and colleague. In Sect. 1.1 his contributions to singularity theory as a pure mathematical discipline are covered, including major extensions of René Thom and John Mather’s theories of smooth and topological equivalence of mappings, stability, sufficiency and versal unfoldings; Milnor fibrations; free and almost free divisors; coherence; bifurcation theory; and partial differential equations. In Sect. 1.2 Jim’s work on medial and skeletal structures is covered; and in Sect. 1.3 his work on the interpretation in images of features, shade, shadow curves and apparent contours, and the manner in which these interact during viewer movement. Finally in Sect. 1.4 Jim’s many contributions to medical image computing are described. He co-advised students and co-wrote many articles with computer scientists on such research topics as the statistics of shape of anatomic objects; segmentation by means of “height ridges” and “connector curves”; skeletal models as an aid to shape statistics; and generalised cylinders as representative of tube-like objects.