Even before steel was a topic of formal study for structural engineers, the brilliant eighteenth century Swiss mathematician and physicist, Leonhard Euler (1707-1783), investigated the theory governing the elastic behaviour of columns, the results of which are incorporated into the American Institute of Steel Construction's (AISC's) Bible: the "Steel Construction Manual". Each semester as the author teaches the introductory undergraduate "Structural Steel Design" course, when arriving at the subject of compression members, he insists on first explaining in detail the mathematical contributions of Euler to the theory of elastic buckling, based on the subject of differential equations--the contents of which constitute this article--before commencing with issues pertaining to engineering design. (Contains 1 table and 8 figures.)