  Traditionally, knot theorists have considered projections of knots where
there are two strands meeting at every crossing. A multi-crossing is a crossing
where more than two strands meet at a single point, such that each strand
bisects the crossing. In this paper we generalize ideas in traditional braid
theory to multi-crossing braids. Our main result is an extension of Alexander's
Theorem. We prove that every link can be put into an $n$-crossing braid form
for any even $n$, and that every link with two or more components can be put
into an $n$-crossing braid form for any $n$. We find relationships between the
$n$-crossing braid indices, or the number of strings necessary to represent a
link in an $n$-crossing braid.
