There are three main primary sources for 15th C European fingerloop braids: 'The Tollemache Book of Secrets', 'Harley MS 2320' and 'Natura Exenterata: Or Nature Unbowelled' (sometimes referred to as 'Serene', the surname of the attributed author of the braiding section). There are also 17th C European fingerloop braids which are quite different from the 15th C ones, but I will not be investigating those.
Cindy Myer has a list of publications for these manuscripts. Most notably, there is a free facsimile and transcription of the braiding section of Serene. Also, there is a free facsimile of the entire Harley MS 2320.
Serene is, perhaps, the most intriguing of the manuscripts. Despite being published in the mid-17th C but its braids are very similar (or the same) as those in the 15th C manuscripts, and unlike those in the other 17th C manuscripts. Its discovery was reported in L-M BRIC News, where you can read more about it and its braids.