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Bitcoin is a crypto-currency, it is maintained by a community and by itself. Bitcoin can be sent or received by anyone with a wallet (and some bitcoin on it).
Exchanges and other solutions allow you to buy bitcoin with dollars, euros and other currencies ...
The value of one bitcoin is fixed by the asking price against the buying one on those exchanges much as the stock market works.
Buying coins can therefore be very expensive when the demand gets high, but there is a way to produce them: it is called mining