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There are basically two lines. Metroline B (Blue Line) and Metroline A(Red Line). Metroline A goes to Vatican City. You need to depart at Cipro/Musei Vaticani station.
MY EXPERIENCE
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We actually planned to take Metroline. But unfortunately there was some accident ... Read review
The ticket for the Vatican Museums costs 14 Euros. If you would like to book one online I provided the link to the Official Vatican Museums Website ... hope that helps ???
Enjoy !
My source: