From Wanderings in Budo by bujinshugyo

九鬼神伝流八法秘剣

後醍醐天皇の守護についていた薬師丸蔵人隆真を始祖とする。後に功により九鬼姓を賜わった。棒、槍、薙刀、手裏剣、体術などの8法に剣術が加わる。剣が特に素晴らしい。当時は戦争の時代だったから殺人剣が多かったが、後に平和な時代になるとそれが活人剣になる。九鬼水軍が船の上で用いたため、腰を低く落として安定した構えが基本になった。

Kukishinden ryū happō biken

The founder Yakushimaru Kurando Takanao was a military governor (shugo) under Emperor Go-Daigo. The Kuki family name was an honour granted later. Kenjutsu is added to the eight methods that include bō, yari, naginata, shuriken and taijutsu. The sword (technique) is especially wonderful. At this time it was an era of war and many people were killed with the sword. Later in the period of peace it became the life saving sword. The Kuki naval forces worked on board ship so the fundamental became dropping the hips for a low stable stance.

九鬼神伝流八法秘剣 Kukishinden ryū happō biken – nine demons divine transmission style, eight methods, secret sword.

The 鬼 ki of kuki is generally translated as demon, however could also mean spirit or ogre (read Oni), more importantly this does not have the evil connotation that the word demon in English (or Judeo-Christian languages) does.
Shinden can variously be translated as ‘teachings of the gods’ ‘teaching conveyed from the gods’ ‘transmitted to the soul’.
Happō can be eight methods, laws or principles, bearing in mind that eight can imply ‘numerous’.

薬師丸蔵人隆真 Yakushimaru Kurando Takanao

薬師丸 Yakushimaru – medicine man, chemical expert
蔵人 Kurando – keeper of imperial archives or a sake brewer
隆真 Takanao – noble truth – the same kanji can also be read as Takamasa, Takanori, Ryūma, Ryūshin and various others – as there is no furigana in the article to indicate the pronunciation I’ve left it as Takanao.

守護 Shugo – military governor in the Kamakura and Muromachi period

後醍醐天皇 Go-Daigo Tennō – the later or second to bear the name Daigo, equivalent of saying Emperor Daigo II. Tennō – heavenly emperor/Emperor of Japan. Lived 1288 – 1339 and reigned from 1318 – 1339.
Go-Daigo in 1336/7 (transition from Kamakura to Muromachi period) set up the southern court and so began the period of two courts Nanboku-chō (Southern and Northern)

1185 – 1333 鎌倉時代 Kamakura jidai
1333 – 1336 建武の新政 Kemmu no Shinsei
1336 – 1573 室町時代 Muromachi jidai
1336 – 1392 南北朝時代 Nanboku-chō jidai (a subdivision of the Muromachi)

The lineage chart shows Kukishinden ryū, originating with Yakushimaru Kurando, passing through Ōoka Kihei Shigenobu to Ishitani Matsutarō Takakage who then passes it on to Takamatsu Toshitsugu to arrive at Hatsumi Masaaki. Note here that in the Japanese article 大岡鬼平重信 Ōoka Kihei Shigenobu is written – usually this person is 大国 Ōkuni Kihei Shigenobu – this may be typo from when the chart was edited for the magazine…