The 11 of September, the "Diada" or
National day of Catalonya.
This day, Catalonya celebrates its defeat by the troops of King Felipe V de Borbón, that day, Catalonya stopped being an independent nation. Many activities and acts are celebrated in all cities of Catalonya.
From September 19th to 24th is the festival of La Mercè, patroness of the city. This is a time of big celebrations with four days of musical performances, parades of giants and big-headed figures, fireworks, the impressive correfocs -- fire creatures costumes that run through many streets of Barcelona -- among other cultural and sport events, and open-air dancing in various places in Barcelona.
If you are already in the city, you will be able to find more information about the events in La Merce booths near Plaçe Catalunya.