Though there are many martial arts that teach effective Knife-fighting (European, Asian, and otherwise), the most popular ones nowadays, and therefore the easiest for you to find, are the Filipino. In particular, Sayoc Kali has developed a reputation lately of being a good knife "attacking" art.
Hawaiian (Lua), Sicilian, Italian, French, Indonesian, Malaysian, and many other martial art systems have effective Knife Fighting training. You may also want to consider the "modern" systems like Kelly McCann, Gunsite, etc.
Given that you are living in New York, you probably have access to an excellent variety. So let me give you more information in terms of how to select a school, rather than just names of styles. Like other forms of fighting, knife fighting is very much INTERACTIVE. You have to be responsive to what the opponent is doing, and vice versa. For that reason, YOU MUST SPAR. Making a million anatomically-targeted cuts through a foam Rubber and duct-tape dummy may make you feel tough and deadly, but it isn't actually going to develop real fighting skill.
Now... you can't truly spar with Live Blades. Anyone who does partner practice with live blades is either doing choreographed stuff or does not care about their own well-being. Sure, they'll give all kinds of reasons (ranging from "realistic appearance and feel" to "learning respect for the blade") for using the live blades. They're idiots. You want to train with something that will actually let you TRY TO CUT YOUR OPPONENT. Typically, training knives are wood, unsharpened aluminum (that was a big trend about ten years ago because it had the glint of metal) or rubber. Knives made of floppy rubber are the worst training tools--knives made of stuff rubber are in my opinion the best. With these, you really only need eye protection.
Good schools often also edge their knives with lipstick or chalk so that they mark each other's clothing for feedback.
If you are interested in learning offensive knife for the purpose of self-defence, you will want to train with some of the more Modern Systems (Kelly McCann is one of the good ones) that teach both draw-from-carry and jurisprudence. If it's more just for sport/hobby, obviously this is unnecessary.
Step by Step Guide Knife Fighting
Buy Now: Seal Knife Fighting Book
This post first appeared on Learn Kung Fu And Chinese Martial Arts Training Techniques, please read the originial post: here
