  This is a review with examples concerning the concepts of affine (in
particular, constant and linear) vector fields and fundamental vector fields on
a manifold. The affine, linear and constant vector fields on a manifold are
shown to be in a bijective correspondence with the fundamental vector fields on
it of respectively general affine, general linear and translation groups
(locally) represented on the manifold via the described in this work left
actions; in a case of the manifolds R^n and C^n, the actions mentioned have the
usual meaning of affine, linear and translation transformations.
