I am really interested in reading them to enrich my knowlodge about Roman society (maybe use them as a primary source for a Future essay ?) I tried looking for them in the library of my university, but all they had was "on the republic", "on the laws" and some speeches, tried looking for them on the internet, no luck either, only PDFs and i would prefer to read a physical copy instead of a PDF, also, which of the 4 groups should i start with ?
There's no single print volume of the letters - it would be massive. There are the Loeb volumes (4 for Atticus, 3 for Ad Fam) if you want to read all 900+, but both Penguin and Oxford World Classics do single volume selections that pick out the most interesting letters. These are probably the best places to start.
They are all freely available online too, of you k ow where to look.
The letters to Atticus are here: http://perseus.uchicago.edu/perseus-cgi/citequery3.pl?dbname=PerseusLatinTexts&query=Cic.%20Att.&getid=1
The letters to his friends (ad fam) are here: http://perseus.uchicago.edu/perseus-cgi/citequery3.pl?dbname=PerseusLatinTexts&query=Cic.%20Fam.&getid=1
The letters to Brutus are here: http://perseus.uchicago.edu/perseus-cgi/citequery3.pl?dbname=PerseusLatinTexts&query=Cic.%20ad%20Brut.&getid=1
Hope this helps!