My parents are both Italian, and both grew up during the 1970s and 80s. My father's from Bologna, specifically, and always goes on about how the Red Brigades destroyed Bologna.
Who were they? What did they do?
There is a profound disconnect between the title of your post and the group you mention. The Red Brigades were a Marxist terrorist group active in Italy from the 70's into the 80's in their original form and structure. Attacks have been carried out in the Red Brigades' name up until 2002.
As a group, they were certainly the most famous and prominent in a quite varied Galaxy of terrorist groups mainly from the left but also from the right operating in Italy in what the Italians call "the years of lead".
What baffles me is that they were totally not fascist and they were not even that active in Bologna. The Red Brigades were mostly active in Milan, Genoa and Rome. The latter because center of Italy's political power, the first two because the strong industrial base made them the natural place to recruit and to find support in the huge factory workers' population.
Bologna was "attacked" quite savagely from neofascist terrorist who blew up the main railway station in the summer of 1980. A neofascist group was accused of having carried out the attack, but denied any involvement and to this day many Italians would not be surprised if you'd venture the idea that the attack was orchestrated by State in what Italians called "strategy of tension", basically a theory that postulated that the state carried out attacks to foster its emergency powers which were vast at the time.
Italy was riddled with killings, kidnappings, and bomb attacks at the time and the news that an Italian terrorist was arrested by the Brazilian police was on today's news, at least the BBC.
For sources there is a ton of stuff in Italian if you have learnt it from your parents. Otherwise, see if you can find "The Red Brigades: A Farewell to Arms," from Xavier Raufer Studies in Conflict and Terrorism, Volume 16, No. 4, October-December 1993 even though is centered on the final phase.