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Prague international airport with code PRG is named Ruzyne like the district where it is located and lies about 17 km north-west from city centre. It was opened in 1937 and grew up to the biggest airport in the middle and eastern Europe. Ruzyne becomes quite busy these days so there are ideas to build a new airport north of Prague in Vodochody to serve low cost companies.
Airport is quite far from the city centre but easily reachable using public transport buses that can take you there in about 40 minutes from centre without any problems. You can catch a taxi or use some paid shuttle bus to the hotel if you want but bare in mind that it is usually quite expensive and you can do the same with the normal public transport ticket for one euro. Taxi drivers in Prague are often mentioned like one of the biggest tourist traps in Prague so be careful. Situation in last years is much better than in the past but still it's better to be prepared.
Bus stations are right in front of the hall of airport and you can catch here these buses: