I am looking for any information on secret societies that may have been active in Italy during the Renaissance (the 14th - 16th centuries). I am particularly looking for groups that may have been involved in the Republic of Florence, or Italy more broadly, but I am also open to researching groups that would have been active across Europe during that time period. I am most curious about what their aims and methods of achieving them might have been. Any help is appreciated. Thank you.
As you may have already noticed, the Knights Templar officially ended in 1312 and the Illuminati was not founded by Adam Weishaupt until 1776 however that doesn't mean to say the legacy of the former didn't exist in the time period you mention.
Following the dissolution and persecution of the Templars, many fled to Scotland. This was a wise move as the current King, Robert the Bruce, had been excommunicated by the Pope and had no interest in following up Papal orders to hunt down Templars and transfer their property to the Hospitallers. Fearful of any attacks, the Templars looked for somewhere they could continue their rite and found a suitable organisation: the masonic guild. The famous Rosslyn Chapel outside of Edinburgh is a perfect example of this hybridity where Templar and masonic symbols sit side by side. Later on, the charter of Scottish masons declares the position of Grandmaster of Scotland descended from William St Clair (who commissioned the chapel) who in turn descended from Hugues de Payens, the Templar founder. In this instance, the remnants of the order had found a new home to entwine with and both contributed and adopted the emergent masonic thought of brotherhood.
To keep the focus on your question, I don't want to delve too much into the spread of Freemasonry outside of Scotland, but it becomes a more apparent and noteworthy force in England especially in the reign of Elizabeth and certainly James I (self-styled "protector of Masons").
Now, to the specific point on secret societies in Italy during the time. Freemasonry as an organised body flourishes in Italy during the 19th Century (The Carbonari in particular) but research is limited for the time period before this. Freemasonry as a concept was not introduced in Italy until 1733 (by an Englishman). However, the topic of Humanism was huge during this period, and many Italian thinkers ranging from Poggio Bracciolini and Coluccio Salutati worked as a group to push their ideas in the courts of Florence and Milan. The reason I am bringing this up is how reliant organised Freemasonry is in the later centuries on the principles Humanism set about, what is pithily summarised amongst modern masons as, "Making good men better" through an appreciation of art and science while promoting education, understanding of oneself and tolerance.
I am open to suggestions but cannot find evidence of secret societies in Italy during this time although the way in which leading humanist figures worked together to install themselves in positions of power throughout the land certainly resembles a focussed group pushing to promote their ideas in all the right places. The impact of their words and deeds allowed later masonic groups (regular or irregular) to coalesce their ideas and leave their mark on the world.
Sources:
Johnson P, The Renaissance (London 2002)
Wilmshurst WL, The Meaning of Masonry (London 1951)
Johnstone M, The Freemasons (London 2016)
Torr G, The Templars (London 2020)