Although there have been many teams on both sides of the law to use the name Brotherhood, the original group were organized by Magneto to establish a nation where mutants could live in harmony without fear of persecution. Magneto and his team of "evil" mutants invaded and occupied the South American nation of San Marco, only to be expelled by the X-Men - but their legacy of terrorism lived on in the so-called Freedom Force; and Brotherhood of Mutants.
Current Version:
The Brotherhood of Mutants (Mesmero's Team)
Former Versions:
The Brotherhood of Evil Mutants (Magneto's Original Team)
The Brotherhood of Evil Mutants (Mutant Force)
The Brotherhood of Evil Mutants (Mystique's Team/Freedom Force)
The Brotherhood of Evil Mutants (Toad's Team)
The Brotherhood of Mutants (Dark Beast's Team)
The Brotherhood of Mutants (Blob's Team)
The Brotherhood of Mutants (Magneto's Third Team)
The Brotherhood of Mutants (Exodus' Team)