During the Muromachi period, the Mino province was very prolific with sword smithing, including the Kanesada and Kanemoto family (you’ll notice some of the other swords also carry those names, including Hijikata’s sword, Izumi no Kami Kanesada; they were all works of the Kanesada family smiths). Kasen Kanesada was forged by the second generation of the Kanesada smiths, which was during the Muromachi period, whose skills as smiths helped establish the reputation of Mino swords. The Kanesada family continued to create sword all the way up to the Edo period, but it is generally agreed that the Sue-Seki smiths that succeeded them weren’t as good.
Nosada (之定) is the alias of Kasen Kanesada’s smith, as he signed the lower part of the character 'Sada' (定) like the character for 'No' (之).
Nosada once published a sutra called Kannon Sutra, the 25th chapter of Lotus Sutra.
The "former master" Kasen refers to in his Book Introduction is Hosokawa Tadaoki (細川忠興), a daimyo who ruled with an iron hand during the Sengoku Period. While Tadaoki was know to be a cultured man and very well-versed in the arts (especially in the art of tea ceremony), he was also know to be a cruel and violent person. As one may infer from reading Kasen's lines, many of Tadaoki's characteristics, both good and bad, have remained with Kasen.
The 36 Immortals of Poetry (三十六歌仙) refers to a a group of 36 Japanese poets from the Heian, Nara, and Asuka period selected by Fujiwara no Kinto as examples of the best of Japanese poets. However, ironically, Kasen Kanesada’s former master, Hosokawa Tadaoki, also happened to KILL 36 of his vassals, so now his name either refers to the 36 Immortals of Poetry, or the 36 dead retainers.
When wounded, Kasen bears a deep slash on his nose. This is reference to the exact wound his former master, Hosokawa Tadaoki, received while trying to save his sister, Hosokawa Iya (細川伊也). Isshiki Yoshiari (一色義有), Iya's husband, was assassinated by Tadaoki as an attempt to save Iya's life. However, in self defense, Iya then pulled out a dagger and attempted to kill Tadaoki, but missed due to Tadaoki's quick reflexes. Instead, Tadaoki escaped death, and only received a deep cut on his nose.
Kasen also bears a cut on his left cheek, a cut Hosokawa Tadaoki also shared. While trying to conquer a castle for the first time, catapult soldiers struck Tadaoki near his cheek and gave him this cut. Oda Nobunaga later praised this scar, claiming it shows a sign of bravery.
Some fanworks depict Kasen and Sayo Samonji together. This may be due to Sayo being given to Fujitaka/Yuusa Hosokawa (細川藤孝/細川幽斎), Tadaoki Hosokawa's father. As such, Kasen and Sayo lived under the same family for a while, before Sayo was eventually sold off by Tadaoki.