Indeed, there you will find many dojo that teach various systems (Karate-Do, Judo, Iaido, Kendo, Jujitsu, Kenjutsu, Ninjitsu, Aikido) and styles (Shorin Ryu Karate, Goju Ryu Karate, Shotokan Karate, Wado Ryu Karate, Kyokushin Kai, Yoshinkai Aikido) and many non-Japanese Martial Arts like Kung Fu, Escrima/Arnis/Kali, Silat, Mixed martial Arts, etc. The question really is what art/discipline will suit you the most. I recommend asking more refined questions, and that way you may be able to discover what art might be more suited for your personal interests Sport, Discipline, Defense, Mind-Body Connection, etc.
It is always a good idea to get introduced to the dojo through contacts or instructors. Showing up at the door unannounced is never a good idea. Most are very generous with those that show the right courtesy and respect.
Also the Japanese were very wise by bringing forms of martial arts from China and Okinawa.
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Dojo is a Japanese word which means "the place of the way". It is the training hall where you study.
I'm assuming you must live in the western hemisphere. The reasons that such a large percentage of the west favors Japanese martial arts are several. One is because most of the Japanese arts are of a more linear and less complicated form which favors the west's more aggressive and direct mentality. Another reason is that many military soldiers brought the Japanese arts back with them from their stations in Okinawa and Japan. The Japanese have, since the Feudal era, been willing to share their arts with the outside world where the Chinese have been very secretive about theirs. Much of the Chinese styles is still misunderstood by the west but with the internet and a more open Chinese mentality, you will surely begin to see more exposure...however it may not be adopted quite so quickly by westerners still. Best wishes.
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Martial arts is the study of warfare and the way of combat. Using a weapon is a martial art. The Marine Corps specifically includes the use of guns and knives in their fighting style.
There is no law to prevent it, but it will depend on the school and the instructor. Some will not teach those that are criminals as they are not considered morally responsible to trust with the techniques of a martial art.