It sounds like something out of a Tolkien book, but Montserrat does really translate to "saw mountain", so named for the distinctive rock formations. It's a great place for a hike and offers stunning views on both sides. The Monastery is a popular destination, but there's also a number of foot paths in the national park.
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Montserrat makes for a great day trip from Barcelona. Catch the local train from Plaza Espanya, which takes you to two points, where you can access the mountain - the options are the rack railway or cable car.
Pack a lunch and enjoy the view from the top.