One group of exceptions is composed of some words of Greek origin. Look at the above phrase, "the Italian system." In Italian we would translate il sistema italiano. In other words, although it ends in -a, it is a boy. In the plural, it returns to the normal scheme, i sistemi.
There are a number of words like this, including il problema, lo schema, il diagramma, il dilemma.
How did this happen? Greek had masculine, feminine and neuter. In the process of fitting one gender scheme into a smaller and different gender scheme, irregularities were bound to occur. Fast forward to the present, where Italian has adopted many words from English, where nouns don't have a gender, generally. The default is the masculine, but other words take the gender of the equivalent in Italian e.g. la mail, the e-mail. The plurals do not change e.g. i bar, i film, i computer, le mail.