>Could it be possible such a thing of a world's single currency?
With the world's currency, I didn't mean the "single" currency. I meant the world's currency like the gold was for many years, or the dollar is nowadays. You used to be able to go anywhere and either buy things with gold or exchange it fairly easily for local currency. Same thing happens nowadays with the dollar. However, the American dollar is losing its preponderance in world trade. The Chinese are pushing really hard to fill that spot with the yuan, this is one of the reasons behind their recent gold fever. [1] Even though, they don't have a gold backed yuan, and probably never will. Gold reserves, together with foreign exchange reserves[2] make a currency stronger, since in case that the Yuan starts to depreciate the Chinese Government can always sell those reserves and buy Yuan's increasing it's demand and consequently increasing its price.
>What is the subject that I should study to understand all of this and stop asking a question like that?
I have an economics background, and I've studied some finance, but I don't think I can give you a good enough answer. If you are really interested I rather you looked online or asked somewhere else (maybe reddit?). Nevertheless the straightforward answer is: Monetary Policy. However, in order to get into monetary policy, I believe that you'd probably need to know the basics about economics, the Mankiw is a good start [4]. Afterwards, I would suggest you to read something from Taleb, maybe The Black Swan, since economics it's full of BS, and this book will serve as a compass. Finally, I would advise you to take the class: Economics of Money and Banking [6] from Columbia on Coursera.
[1] http://www.ibtimes.com/chinas-gold-fever-rises-showing-no-si...
[2] China has the highest foreign exchange reserve in the world http://en.wikipedia.org/wiki/Foreign_exchange_reserves_of_th...
[3] http://en.wikipedia.org/wiki/Monetary_policy
[4] http://www.amazon.com/Principles-Economics-N-Gregory-Mankiw/... If you are interested don't get scared by the price tag, buy any older editions which are almost as good as this one and will cost you a fraction.
[5] http://www.amazon.com/The-Black-Swan-Improbable-Robustness/d...
[6] https://class.coursera.org/money-002