Pike and Musket Society
The Pike and Musket Society or the Routiers are a living history organisation whose focus is on the military aspects of 17th century Europe. It was formed in Australia but has international associations.
They concentrate on the Trained Bands (or "Trayned Bandes" if you prefer) of London during the period of the English Civil War. Even more specifically, the Second Captain's Company of the Green Band. The Society's aim is for as much historical accuracy as is practicable. Clothing, weapons and accoutrements are carefully reconstructed, based on historical research, preferably using primary (period) sources.
Their reasoning is "to take historical re-enactment seriously, and ourselves seriously not at all!" - the opposite tack to some other organisations.
The above description is based on the content of the old website http://www.theroutiers.org/whatis.htm [dead link August 2014]
The website has since been updated with a new "About us" section. http://theroutiers.org/wp/about-us/