  A point particle of mass $\mu$ moving on a geodesic creates a perturbation
$h_{ab}$, of the spacetime metric $g_{ab}$, that diverges at the particle.
Simple expressions are given for the singular $\mu/r$ part of $h_{ab}$ and its
distortion caused by the spacetime. This singular part $h^\SS_{ab}$ is
described in different coordinate systems and in different gauges. Subtracting
$h^\SS_{ab}$ from $h_{ab}$ leaves a regular remainder $h^\R_{ab}$. The
self-force on the particle from its own gravitational field adjusts the world
line at $\Or(\mu)$ to be a geodesic of $g_{ab}+h^\R_{ab}$; this adjustment
includes all of the effects of radiation reaction. For the case that the
particle is a small non-rotating black hole, we give a uniformly valid
approximation to a solution of the Einstein equations, with a remainder of
$\Or(\mu^2)$ as $\mu\to0$.
  An example presents the actual steps involved in a self-force calculation.
Gauge freedom introduces ambiguity in perturbation analysis. However,
physically interesting problems avoid this ambiguity.
