  We present a fundamental theory of curves in the affine plane and the affine
space, equipped with the general-affine groups ${\rm GA}(2)={\rm GL}(2,{\bf
R})\ltimes {\bf R}^2$ and ${\rm GA}(3)={\rm GL}(3,{\bf R})\ltimes {\bf R}^3$,
respectively. We define general-affine length parameter and curvatures and show
how such invariants determine the curve up to general-affine motions. We then
study the extremal problem of the general-affine length functional and derive a
variational formula. We give several examples of curves and also discuss some
relations with equiaffine treatment and projective treatment of curves.
