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I'm a little scared to post this because there's a group of guys on here who dedicate their lives to complaining about Barcelona's public transport, but... I think it's pretty good.
The whole city is covered by the metro, plus the nearest adjoining big towns/cities (Badalona, l'Hospitalet, Cornella, El Prat, Santa Coloma). The busiest lines run at a frequency of less than 3 minutes at peak times.
Then there are trains to all the surrounding towns and cities, most of which have pretty acceptable frequency (30 minutes or less) given that they're not serving the most populated areas. There are also a lot of buses although I find the metro is almost always faster.
The best part is that a 10 trip ticket for the central zone only costs €10, and a 3 month unlimited 1 zone ticket costs €142. I probably make 25-30 journeys per week so it works out ridiculously cheap for me.