The n-th braid group consist of all different ways n strings can be braided. The generators are all the over-crossings and under-crossings of neighbouring strings. They can be also imagined as world lines of n particles in 2 dimensions which changes its order.
Examples
The generators 
and 
:
And the transformation like:
is not a braid.
Applications
The braid group plays key-role in the topological computing.
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