Most explosives were ironically enough discovered by mistake when trying to make a medicine. Black powder is supposed to have been invented by Taoist monks, who wanted to create a life elixire. Nitroglycerin is actually used as a medicine and is never used as an explosive on its own anymore, except in demonstrations. Most "modern" explosives were invented by Germans in the late 19th Century, including the ones that terrorists and people making bombs at home for the fun of it use. TNT was invented my the German-American Windelbrand. There are very few nations that have invented explosives. Non-German inventors of modern explosives were either Italian, American, French, Swiss or Swedish. Most explosives contain nitrogen in some form. One of the few exceptions is the very powerful, easy-made and dangerous tricycloacetonperoxide.
