In the early 1950's, Gerald Gardner developed an initiatory tradition of Witchcraft based on teachings from Freemasonry, Aliester Crowley and the New Forest coven he was a member of. Gerald Gardner, with the help of Doreen Valiente and others, laid the foundation work of modern Wicca and is sometimes referred to as the Father (Grandfather?) of Modern Wicca.
Gardnerian covens are lead by a High Priestess and have three degrees of initiation. They worship a Goddess and a Horned God, while stressing the importance of polarity, fertility and the cycles of life. The Eight Seasonal Sabbats are observed as well as Esbats and Rites of Passage. The tradition is geared more toward covens, who usually work skyclad, but has presented some solitaire works.
Gardnerians tend to be a close knit group and strictly protect their oathbound material. Thus it will be more difficult in locating and joining a true Gardnerian coven than a local Eclectic group.
Founded by Alex Sanders in the early 1960's, England, as an offshoot of the Gardnerian Tradition, it utilizes many of the tools and ritual practices of its predecessor, though in different ways at times. Other differences would include the Deity names and the emphasis on more occult and magical practices.
Founded in 1973 by Raymond Buckland, Seax-Wicca bases its tradition on the Saxon mythology and practices. "Seax" is a word meaning dagger or knife. The tradition recognizes both coven initiations and self-initiations as valid for this path. The covens are usually lead by both a High Priest and High Priestess, holding open rituals and each coven determines for themselves whether to work robed or skyclad. Decisions for the coven are made by the coven instead of just one or two people.
More to come!