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You can either take a bus, a van, a kombi or a "lotada" (this is one is basically an ordinary car) depending on where ya want to go. From time to time its being developed, with certain ways of destination and routes, special traffic project for the World Cup 2014. And the state fare is kind of high being R$2,50. If its safe, well, not so safe. Pay attention because some robbers assault these kind of transportations, mainly buses. Just be alert and its cool.

Is the same thing in Paris...you have lots of thives.
Rio isn't a dangerous city.Not more others bigs cities.

Compared to Sao Paulo, Rio's subway system is not that developed and comprehensive. Right now, it only covers the northern, center and southern part of Rio City. Construction of the line that will link the western part is still on going in preparation for Rio2016 which mostly will be constructed in Barra da Tijuca in the west.
I use both the metro (subway) and buses everyday and luckily never had any bad experience with thieves but you should expect the constant traffic during rush hours.
If you have a CPF, you could buy a Bilhete Unico Carioca (a prepaid card). This can give you a benefit of transferring to another bus line within 2 hours without paying again the basic fare of R$2.50 which is around 1.50 USD.

Look this site: sognandobrasile.com/trasporti-brasile/treni-metro-brasile/