The Alexandrian tradition comes out of the coven started by Alex Sanders in England.
Alex claims he was initiated by his grandmother in 1933, but many Alexandrian rituals are almost identical to Gardnerian ones, with a little more emphasis on ceremonial magic.
The tradition's rituals, while basically Gardnerian, are modified with many Judeo-christian and Ceremonial Magick elements.
Covens work skyclad. The eight Sabbats are observed and the Goddess and God are observed.
Sanders did much to popularize the Craft but perhaps one of his best acts was to initiate Stewart Farrar.
Farrar later formed his own coven and went his own way.
Mary Nesnick, an American who was initiated into both Gardnerian and Alexandrian traditions, combined them in 1972 and created a new tradition called Algard.