I've done some reading and I've discovered that our modern system of music theory (I'm looking at you Roman numeral analysis) is not the same system that most of the great composers used, including the "Big Three": Mozart, Bach, and Beethoven. Apparently, they favored the system of thoroughbass. Bach himself was supposedly against Rameau's theory of harmony, from which our modern system is derived.
I did a little more digging and I managed to find some good texts that I would like to study; however, there are just so many to choose from. It seems that thoroughbass was broken down into two different goals, writing down a realization (taking as much time as necessary to do this), and realizing a figured bass extemporaneously at a keyboard, as if sight reading.
My question is this: What is the modern approach to teaching/learning thoroughbass?
I wonder if a few particular items are still used in modern curricula:
It seems to me that the C.P.E Bach essay, as well as J.S. Bach's precepts and principles, are well known, but are a little difficult. There's also the Albrechtsberger book and a book that seems to be written by Mozart on the subject, though I don't know if the claim of Mozart's authorship is reliable.
Ultimately, I would like to be able to look at a figured bass and be able to provide a realization, either written down or extemporized, in any key.