Which Baroque composers were also instructors?

In the Baroque era, musicians usually did not work "freelance." They worked for either the church or the court (Royal Court). They were payed and treated as any servant was, and rarely amassed a great amount of wealth. (Handel is an exception, at the time of his death, his estate was worth 20000 pounds, which was a huge amount back then)

A musician hired for the court was expected to:

write music for performance.

Organize performances and musical activities.

Teach music to members of the Royal (or noble) family.

The composer you mentioned, Vivaldi, worked at the Conservatorio dell'Ospedale della Pietà, which is the music shcool of the Ospedale della Pietà (a foundling home for girls). Vivaldi was the master violin tutor at the Ospedale della Pieta from 1704, and chief composer from 1713 until he left Venice in 1740. Most of the music he wrote during this period was for the school, and even when he was not in venice, he would send music back to them.

The Hindemith "Elementary Training" book (which is not "elementary" in ANY way) is a fantastic book, but it is NOT what you're looking for. Music theory/fundamentals books: There's a really nice book by Joseph Straus called "Elements of Music" which you could think about getting. It's designed as a book to be used in a class, but you could work through it on your own, if you're diligent about it. Famous composer information: If you live anywhere near a college with a music department, then go to their library and look in the New Grove Dictionary of Music and Musicians. The articles are probably too long and in-depth if you're just looking for basic information about composers, but it's a wonderful resource. Don't forget the most obvious source -- your teacher(s). If your teacher is asking you questions about things you don't know, then ask him/her if you can work some theory into your lessons. Your guitar teacher, especially, should be a big help in this. Good luck!

However, Beethoven was not Baroque.

Bach may possibly be what you are looking for- he was employed by the church/cathedral to compose and perform music full time. He probably would have taught junoir organ scholars and he may have even conducted choirs and small orchestras.

Of course, it was a good way to make a living. In the Baroque period, the most successful composers were musicians full time for most of their lives.

I hope I have answered your question!

At that time, there were no professional performers, composers, or teachers.

Rather, there were professional musicians, who were expected to do all three.

Beethoven was the first person who dared to become a professional composer, and he did not always feel secure in his venture.