There are a number of variations to the basic and most well-known set of runes, called the Futhark, inluding Anglo-Saxon and Germanic runes. Scandinavian runes, which are unrelated to the Anglo-Saxon runes in their development, can be divided into three categories.

The first period starts with the development of runes, which has been estimated at around A.D. 175, but as far back as 500 B.C. by some, and lasts until the eighth century. This is referred to as the Primitive Norse Period. The runic inscriptions found from this period are primarily in Primitive Old Norse or Primitive Germanic languages, and the runes are those of the Elder Futhark. All inscriptions are uninfluenced by Christianity as yet.
Note: Lore states that the ancient god Odin disovered the runes after starving and depriving himself and gouging out one of his eyes, which sort of disagrees with this more practical number. Who knows, this is just what the archaeological "experts" have said.

The second period, called the Late Primitive Period or sometimes the Viking period, began in the eighth century and ends around 1075. Mostly Younger Futhark runes are found, and some of the inscriptions found are confusing, since the Anglo-Saxon Futhork had been brought over by British scholars. The inscriptions during this period show both non-Christian and Christian subject matter, as Christianity began to spread Northward.

The third period, called the Medieval Period, endures until the middle of the fourteenth century, when runic inscriptions vanish, largely due to the intolerant pressure from the Catholic church. The magical usage of the runes is at its maximum during this period, mixing with other Pagan magics as well as Christian.

Recently, a resurgence of interest in runes and their lore has occurred, and many interesting texts are more readily available. If you would learn more, try these: