was a province of Japan in the area of Japan that is today Yamanashi Prefecture. Kai bordered on Sagami, Suruga, Shinano and Musashi Provinces. Its abbreviated form name was . The origin of its name is uncertain. It lies in central Honshà «, west of Tokyo, in a landlocked mountainous region that includes Mount Fuji along its border with modern Shizuoka Prefecture.
Kai was one of the original provinces of Japan established in the Nara period under the Taihà  Code. The original capital of the province was located in what is now Fuefuki. Under the Engishiki classification system, Kai was ranked as a "superior country" (ä¸Âå½) in terms of importance, and one of the 16 "middle countries" (ä¸Âå½) in terms of distance from the capital. Although not directly on the Tà Âkaidà Â, it was also included as one of the Tà Âkaidà  provinces.
Numerous remains from the Kofun period have been found in Kai. During the Heian period, the area came under the control of the Kai Genji, who controlled the province throughout the Kamakura period. During the Sengoku period, a branch of the clan, the Takeda clan rose to prominence. The warlord Takeda Shingen, ruled Kai from his stronghold at Kà Âfu and expanded the holdings of the clan to include Shinano and Suruga Provinces, and engaged in constant warfare against the Uesugi clan in Echigo Province. After the Takeda were defeated by a coalition led by Oda Nobunaga and Tokugawa Ieyasu, Kai Province came briefly under the rule of NobunagaâÂÂs retainer Kawajiri Hidetaka. After NobunagaâÂÂs assassination at the Honnà Â-ji Incident, the province was contested between Tokugawa Ieyasu and the Go-Hà Âjà  clan based in Odawara. The Tokugawa clan, the Uesugi clan and the Hà Âjà  clan each aspired to seize the vast area in Shinano Province, Ueno region, and Kai Province, which ruled by the remnants of the many small clans formerly serving Takeda clan, following of disorder post death of Nobunaga, at the same time with Ieyasu departure an army of 8,000 soldiers to those disputed region. This caused the triangle conflict between those three factions in the event which dubbed by historians as broke out. As the war turned in favor of Tokugawa clan, combined with the defection of Sanada Masayuki to the Tokugawa faction, the Hà Âjà  clan now negotiate truce with Ieyasu. The Hà Âjà  clan then sent Hà Âjà  Ujinobu as representative, while the Tokugawa sent Ii Naomasa as representative for the pre eliminary meetings. Furthermore, in October, representatives from the Oda clan such as Oda Nobukatsu, Oda Nobutaka, and Toyotomi mediated the negotiation until the truce officially concluded.
However, after the destruction of the Go-Hà Âjà  by Toyotomi Hideyoshi in 1590, the province was ruled by a succession of Toyotomi loyalists.
With the establishment of the Tokugawa shogunate, Kai was regarded as strategically important to the defense of Edo due to its position between the Tà Âkaidà  and Nakasendà  highways, which were connected through Kai Province by the Kà Âshà « Kaidà Â. Kai Province was entrusted briefly to Tokugawa clan members or the highly trusted Yanagisawa clan from 1705-1724 as Kà Âfu Domain, but for the most part was retained as tenryà  territory ruled directly by the shogunate through a succession of hatamoto-class daikan.
After the Meiji Restoration, Kai province was renamed KÃ Âfu Prefecture in 1869. With the abolition of the han system in 1871, it was renamed Yamanashi Prefecture.
Kai Province consisted of nine districts (originally consisted of traditionally four):