On algebras,manifolds, and fibre bundles in physics

This article surveys the mathematical or physical aspects of algebraic realizations, fibre bundles, supermanifolds, super Lie groups, and super Lie algebras.An expanded and modified version of an invited talk given at the Special Session on Nonassociative Algebras and Their Connections with Physics, at the 749th meeting of the American Mathematical Society, Purdue University, October 29, 1977.