Unfortunately I do not know very little of the lineage of our style of kenjutsu, nor do I know the name of the style that we do. We just call it kenjutsu. From what I have seen we do the same basic techniques that other styles do. We do not have as many kata as other styles however. The following is what I know of our style of kenjutsu.
The practice of kenjutsu has many things to offer, it may not seem very practical by looking at the surface. This reminds me of a quote I once read: “The reflection on a pool does not reveal its depth.” The same is true with kenjutsu. It is true that you will probably never get in a sword fight. But learning how to use the sword has many other benefits, besides fantasizing about being a samurai and fighting a duel to the death.
In kenjutsu there is a lot of focus on footwork, footwork is very important in any martial art. Good footwork not only helps to get your whole body into the cut but it also allows you to remain balanced. If you are ever off balance doing a kenjutsu technique you are using bad footwork. This helps in other martial arts making it harder to throw you, and harder for you to get stuck with your feet in a bad position to defend or attack. Kenjutsu also helps improve your timing, coordination, and speed. All of this is just the physical benefit of kenjutsu practice.
Practicing kenjutsu also helps you mentally in many ways. Although we are pretty laid back as far as formality goes, your training should be deadly serious. What I mean by this is; in kenjutsu you must realize that most of our techniques and teachings are designed to kill your opponent. When doing two-person work, kata, and sparring your are practicing to kill. Especially with two-person work and sparring, not only are you practicing to kill your opponent but he is practicing to kill you also. A samurai was to die in service of his lord, and not fear death. By training with deadly seriousness it will help you to also to not fear death. Once you are not afraid to die you will truly live. A lot of people think that this meant the samurai foolishly gave up their lives. This is not true. A samurai was of better service to his lord if he was alive, but at the same time he was not afraid to die for his lord, or his lords cause. When you no longer fear death you will realize how great life is, and problems that you thought were huge before, will seem so minor that you will wonder why you got so stressed out about them. Also you should think about the morality of killing someone. Would you kill this person for no reason, take him or her away from their family possibly destroying the entire family? This probably sounds strange but by thinking this way hopefully you will become more compassionate. Hopefully you will realize that life is very precious, and you should try to avoid conflict whenever possible. You never know how angry someone will get for the littlest strike against their “honor”. A lot of people confuse their honor with “face” but that is a whole different story. You might be saying “But I would never make someone angry enough to kill me?!” well there is road rage and high school shootings, neither of which make much sense to me. But by training with deadly seriousness and thinking about being compassionate you will become more polite also. By being polite it will be harder to anger someone to the extent that they want to kill you. The benefits of kenjutsu, or any martial art take lots of hard work, time, and dedication to achieve. That doesn't mean you can't have fun. Fun is another benefit of kenjutsu that is often overlooked.
You should never touch someone else's sword without asking permission first. There are a few reasons for this. One you could damage the sword accidentally, although you might do that even with the owners permission it would be easier to forgive you if they gave you permission first. Another reason is a sword is a dangerous weapon and you could hurt yourself if you don't know what your doing. Also you should never touch the blade of a sword, the oil on your hands is bad for the blade, and fingerprints are hard to get off the blade. Not to mention you could cut yourself. If you ever do need to touch the blade for some reason you should use a piece of cloth or paper.
Here are some links to other kenjutsu styles.