  This is a systematic introduction for physicists to the theory of algebras
and groups with braid statistics, as developed over the last three years by the
author. There are braided lines, braided planes, braided matrices and braided
groups all in analogy with superlines, superplanes etc. The main idea is that
the bose-fermi $\pm1$ statistics between Grassmannn coordinates is now replaced
by a general braid statistics $\Psi$, typically given by a Yang-Baxter matrix
$R$. Most of the algebraic proofs are best done by drawing knot and tangle
diagrams, yet most constructions in supersymmetry appear to generalise well.
Particles of braid statistics exist and can be expected to be described in this
way. At the same time, we find many applications to ordinary quantum group
theory: how to make quantum-group covariant (braided) tensor products and spin
chains, action-angle variables for quantum groups, vector addition on
$q$-Minkowski space and a semidirect product q-Poincar\'e group are among the
main applications so far. Every quantum group can be viewed as a braided group,
so the theory contains quantum group theory as well as supersymmetry. There
also appears to be a rich theory of braided geometry, more general than
super-geometry and including aspects of quantum geometry. Braided-derivations
obey a braided-Leibniz rule and recover the usual Jackson $q$-derivative as the
1-dimensional case.
