Recently talking about British Traditional Wicca led me to put a bit more information together about the Alexandrian tradition to help complete the discussion a little more. It tends to get overshadowed by Gardnerian Wicca.
As you can probably guess, the tradition was named for its founder, Alex Sanders (though some claim its really named after the famed Library of Alexandria). Sanders was a prominent figure in the witchcraft community during the 60s and 70s, and he brought a lot of Wiccan information out to the public through interviews and publications. He was in the spotlight so much, he earned the dubious nickname "King of the Witches".
It was all the fame that eventually caused Alex and some of his followers to leave their original covens to branch off to their own path. The first Alexandrian Wicca coven was known as the London Coven.
Since he came from the original Gardnerian coven, there is a lot of similarity between the two forms of Wicca. So I suggest you first read the background on Gardnerian Wicca, and then I can outline the differences rather than repeat all the similarities again.
Of course, the problem still remains that this is a mystery tradition with much of the details held in secret between coven members. Only initiates in the traditions will know the real differences between the two, and that sadly does not personally include me at the moment.
Overall, Alexandrian covens tend to be a bit less formal and more eclectic than strict Gardnerian ones, though with a stronger emphasis on Ceremonial Magick and rituals. One smaller difference is that Alexandrians use an athame to represent fire and the wand for air (reversing the Gardnerian view of these tools).
Books written by the Farrars and Sanders himself are good introductions into Alexandrian traditions, but they are not complete. Many inner details are still oathbound and not available to the general public outside of a coven setting.
Probably not the most helpful article ever, but at least now you know that Alexandrian Wicca is very close to Gardnerian Wicca and that you'll need to join a coven to know more.