  This article provides a self contained overview of the geometry and dynamics
of relativistic brane models, of the category that includes point particle,
string, and membrane representations for phenomena that can be considered as
being confined to a worldsheet of the corresponding dimension (respectively
one, two, and three) in a thin limit approximation in an ordinary 4 dimensional
spacetime background. This category also includes ``brane world'' models that
treat the observed universe as a 3-brane in 5 or higher dimensional background.
The first sections are concerned with purely kinematic aspects: it is shown
how, to second differential order, the geometry (and in particular the inner
and outer curvature) of a brane worldsheet of arbitrary dimension is
describable in terms of the first, second, and third fundamental tensor. The
later sections show how -- to lowest order in the thin limit -- the evolution
of such a brane worldsheet will always be governed by a simple tensorial
equation of motion whose left hand side is the contraction of the relevant
surface stress tensor $ bar T^{\mu\nu}$ with the (geometrically defined) second
fundamental tensor $K_{\mu\nu}{^\rho}$, while the right hand side will simply
vanish in the case of free motion and will otherwise be just the orthogonal
projection of any external force density that may happen to act on the brane.
