It is a subject that is built from certain foundations and then reaches its peak in the person of Israel Salanter.
The essence of Musar is the idea that everyone should learn one of five basic books of Morality written during the Middle ages on the subject of ethics. To this is added the idea of the subconscious that Israel Salanter borrowed from Schopenhauer. The idea is this:by daily review of these books something of their ideas on ethics gets into the subconscious.
But there are a few unstated insights about this idea that are not stated explicitly. One is a very well known Jewish idea but sadly enough Christians seem to be completely unaware of it.It is the idea that during the Middle Ages people were very careful in what they wrote about philosophy and theological subjects. It is what is called in the Jewish world "Rishonim." It means not that people that wrote then were somehow divinely inspired.It does not mean that. It means that they were extremely careful not to write things that would be logical fallacies. This care and caution was shot to smithereens after the time of Hume who in spite of his great and original thought wrote in basic logically fallacies--so much so that it leaves me wondering if he did so on purpose. since then philosophy is dominated by circular reasoning including Hegel who assumes what he wants to prove. [As Habermas noted that in the phenomenology Hegel tries to prove the identity of Subject and Object--but in fact he assumes it right from the start.] You never see this in writing from Jewish Christian or Muslim philosophers from the Middle Ages.
Christians probably have some equivalent of Jewish Musar from the middle ages but i am not sure of what it could be. They should probably make and effort to dig it up. What I means is Musar may be based on philosophical thought but these are books that are specifically about morality, not philosophy.
This means that learning Aquinas would not be in this category of Musar.
At any rate back to the Jewish subject of Musar
This subject was highly misunderstood after Israel Salanter. The reason was that the divide between reform Jews and orthodox Jews had grown to such a degree that the emphasis of people like Maimonides on science and philosophy was ignored. So Musar was taken to be a radical anti science anti philosophy doctrine and any books from the actual Musar books that said differently were explained away.
Something is curious about Musar in terms of the treatment of the soul. This subject is too big for this blog right now. But just briefly let me mention that the Jewish treatment of the soul was influenced by the brethren of purity. In fact the whole move away from Neo Platonic thought in Ibn Ezra [who accepts the Neo Platonic scheme point black] and Saadia Geon to Aristotelian thought in Maimonides seems to have been influenced by the Muslim philosophers of those times. But as we reach the Musar Movement of Israel Salanter it seems the idea of the soul have changed to the general Christian concept of an ethereal essence.
I really have no time to go into this right now but it would make a great term paper.
Reb Israel did borrow the idea of the self from Hobbes and the subconsciousness from Schopenhauer and other ideas developed by Enlightenment philosophers. Later on the Musar movement made a move to deny this debt. The prime directive in the Jewish Orthodox would today is never acknowledge a debt to a Christin or Muslim thinker.
The Rambam (Maimonides) and Saadia Geon always acknowledged from where they borrowed their ideas. That is what makes them interesting and it helps to see what they are adding or improving on.