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The term Koryu, along with the terms Kobudo, Kobujutsu and Bugei, is used in Japan so that a difference can be made between classical and modern martial arts (gendai budo).
Koryu is consisted of two ideograms (kanji): Ko 古 – old, ancient, and Ryu 流 – tradition, school. A rough translation would be „old school“ or „ancient tradition“.
Kobudo is consisted of three kanji: 古武道 and the loose translation would be „old martial ways“.
We would translate kobujutsu 古武術 as „ancient martial sciences or crafts“.
Bugei 武芸  is translated as „martial arts“.
In any case, these terms point to the classical Japanese martial styles that were used before the modernization of Japan (before 1868), when actually the samurai class was forbidden and removed as a remainder of the feudal period.
During the feudal reign in Japan, the martial schools (ryu-ha) were developed so they can secure the survival or a better position of the warriors (bushi) that were in the service of several principalities (han) led by a daimyo (the rulers of a land). At the beginning, the arts often were otome-ryu (a tradition that is transferred in the home), although later they were frequently taught to other samurai in the principality, so that survival of the whole community can be guaranteed. 
Finally, with the beginning of the Meiji period (1868), when many of the descendants of the schools remained unemployed as a result of the rejection of the samurai class, the arts started to be publicly taught as one of the ways to survive in those conditions. Precisely for that reason, many ryu-ha endured through the time, so today we have the opportunity to learn and feel the samurai spirit from feudal Japan.