The circle above indicates the time we discuss in this section
Introduction Of The Five Main Sword School (Den)
There are five major sword schools (Den): Yamashiro Den (山城), Bizen Den (備前), Soshu Den (相州), Yamato Den (大和), and Mino Den (美濃). During the Heian period, Yamashiro Den was the main and most active school. A school called Ko-bizen (meaning Old Bizen) during the Heian period is a part of Bizen Den. However, we take the Ko-bizen separately since their style is slightly different from the later Bizen Den but somewhat close to the Yamashiro Den as we see it later.
During the Heian period, the swordsmiths of Yamashiro Den lived around Kyoto, the capital of Japan then. In the early Kamakura period, Yamashiro Den maintained the similar sword style they created in the Heian period. Bizen Den appeared in the middle Kamakura period. Soshu Den appeared in the late Kamakura period in Kamakura area. Mino Den appeared in the Muromachi period, which comes much later.
The Early Kamakura Period (鎌倉)
We divide the Kamakura period into three stages: the early, the middle, and the late Kamakura period. The sword style in the early Kamakura period was almost the same as in the previous Heian period. Yamashiro Den was continuously the most active school through the early Kamakura period.
The Middle Kamakura Period
In the middle Kamakura period, we have three different styles of the sword to discuss: the Yamashiro Den style, the Bizen Den style, and the Ikubi-kissaki (猪首切先) style, which was new at that time. We can say that among the Ikubi-kissaki swords, seldom sees the mediocre sword.
The previous section described the Kamakura Bakufu (鎌倉幕府: government) had political and military power, yet the emperor was still on the throne in Kyoto. Emperor Gotoba raised an army and attacked the Kamakura government to regain political control. This war (1221) is called Jyokyu-no-Ran (承久の乱). The war changed the look of swords to a sturdier shape. This style is what we call the Ikubi-kissaki.
The Late Kamakura Period (after the Mongolian Invasion)
During the late Kamakura Period, Soshu Den emerged in addition to Yamashiro Den and Bizen Den. After the two Mongolian Invasions called Genko (元寇) in 1274 and 1281, longer and broader swords with longer Kissaki began to appear. The Soshu Den swordsmiths forged this type of sword
Engravings on Sword
Engravings on a sword in the Ko-to era (Heian to Keicho era) has three purposes. One is to reduce the weight of the sword. Hi, Bohi, Gomabashi (wide, narrow, short, or long grooves) are examples. The second is for religious purposes, for which swordsmiths often carved Buddhistic figures. The third is for decoration. In the Shin-to era (from Keicho time and after), it became mainly for decoration purposes.
The figures below are examples of the engravings.
Suken Bonji (sanskrit) Gomabashi Hi
Study of Japanese Sword 