What is a set of Jewish commentaries called?

Answer 1

The Talmud.

Religious Jews live by the Torah, by obeying its commands and beliefs. There are hundreds of examples. However, the Torah "as is" isn't exactly what Judaism observes. Rather, It's the Torah together with the details provided in the Talmud, which is the Oral Law that was handed down together with the laws of Moses. Otherwise, the verses of the Torah often lack enough detail to be fulfilled as is.
For instance, the law of honest weights and measures (Leviticus 19:36) does not state if any deviation is permitted. How often do the scales need calibration? What is the penalty for overcharging? Etc.
The laws (Deuteronomy ch.17) concerning the judges (Torah-sages; Sanhedrin) do not say what exactly constitutes bribery (Deuteronomy 16:19). Is it bribery if I compliment a judge before the court case but do not give a gift? And myriad other questions: How many judges are a quorum for Torah-courts? Is there a time limit for court cases? Etc.
The laws concerning restitution for damages (Exodus ch.22) do not tell us if payment needs to be made for emotional stress.
The key Hebrew word in Exodus 22:4 can mean either fire or cattle. Which is it? Or is it both?
In Exodus 22:5, is there a difference in restitution between deliberate and accidental spreading of fire?
So it is the function of the Talmud to expand upon the details, and to give us the precedents and Torah-tools for determining new cases in the future.

More information

• The Talmud contains the Oral Torah of the Jewish people.
  
• The Talmud serves to clarify the brief verses of the Torah and Tanakh (Hebrew Bible).
  
• The Talmud, after the Hebrew Bible, is considered the primary text of Jewish learning.
  
• The Talmud contains, in addition to Torah-matters, some mathematics, geometry and trigonometry, medicine, astronomy, and advice on a large range of problems and situations.
  
• The Talmud includes information on the lives and personalities of the Sages, from Abraham down to the writing of the Talmud.
  
• The Talmud was kept entirely orally, and learned by heart, from the time of Moses until it was written 1800 years later (1500 years ago).

• The Talmud contains the Mishna (relatively brief paragraphs of law, in Hebrew) and Gemara (explanations of the Mishna, in Aramaic and Hebrew).
  
• The Talmud has thousands of published commentaries.
  
• The Talmud contains 63 tractates (volumes) in 2711 leaves (double pages). New printed editions maintain the same pagination as earlier ones.
  
• The Talmud has been banned, censored and burned many times by enemies of the Jews.

Some of its books are:
A tractate (volume) about the daily blessings (Berakhot)
A tractate about Shabbat
A tractate about Passover (Pesachim)
A tractate about Rosh Hashanah
A tractate about Yom Kippur (Yoma)
A tractate about Purim (Megillah)
A tractate about marriage (Ketubot)
A tractate about vows (Nedarim)
A tractate about divorce (Gittin)
Three tractates containing laws of torts, damages, property etc. (the three Bavot)
A tractate about Jewish courts (Sanhedrin)
A tractate about the prohibition of idolatry (Avodah Zarah)
A tractate about the offerings (Zevachim)
A tractate about the laws of keeping kosher (Chullin).

Answer 2

There are many commentaries but the most important ones are found in the Talmud.

Answer 3

tehillim, or psalms written by King David.

Answer:The Talmud.