Question: 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?**

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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.

Answer: 
As someone who is currently learning to play from figured bass on the harpsichord, I can recommend starting with the book "Continuo Playing According to Handel: His figured bass exercises" edited and with commentary by David Ledbetter.

The exercises start with just root position chords for the first exercise and mostly add one new concept with each exercise. While the exercises (basses) are by Handel, the commentary, guidance and sample realizations are by the editor. He gives guidance on realizing the basses in the standard 1+3 style (1 "voice" in the LH, 3 in the RH). This is a good place to start, but be aware that it doesn't stop there – skilled harpsichordists will often use more voices, as well as having more than one voice in the LH.

One thing that I feel would have been useful to add to the book is transposed versions of the exercises (particularly the early ones) to build fluency in different keys. However, you can make these yourself either with software or by writing them out by hand.

It may be helpful to know that the editor has a page of corrections and additions to the book: <https://davidledbetter-music.com/continuo-playing/>
For myself and others a list of terms... 

* figured bass: a system to represent chords, synonymous with 'thorough bass'
* basso continuo : executing a figured bass
* partimenti : figured bass exercises to teach students harmony and practice basso continuo performance

[The Art of Partimento](https://rads.stackoverflow.com/amzn/click/com/0195394208): History, Theory, and Practice by Giorgio Sanguinetti 

This isn't a collection of partmenti, but rather a text about the method and its history. Lots of musical illustrations, but not really a book from which to practice.

[The Langloz Manuscript: Fugal Improvisation through Figured Bass by William Renwick (Author)](https://rads.stackoverflow.com/amzn/click/com/0198167296)

This may not have a lot of immediate practical value, but it's very interesting to read about how partimenti and figured bass as the foundation for the master skill of fugue improvization.