Teaching is more important than both learning and practicing [although, obviously, not a substitute for either]: Bava Kamma 17a
On one who learns without teaching: Rosh HaShanah 23a
On one who teaches in a place where there are no other scholars: Rosh HaShanah 23a
The gravity of altering the Torah, such as by converting concrete commandments into abstract ideas: Megillah 25a
Teaching in a public place: Moed Katan 16a-b
Having a Mourner teach, although he is ordinarily forbidden to learn Torah, if he is needed: Moed Katan 21a
Publically teaching the laws of Pesach/all of the holidays, beginning 2 weeks/30 days beforehand: Pesachim 6a-b; Rosh HaShanah 7a
Publically teaching at the special bi-annual gatherings of learning [Kallah]: Moed Katan 16b
Hiding the secret sections of Torah: Pesachim 119a
Against teaching an ignorant [, practicing] judge: Shabbat 139a
Permission to split a verse while teaching it: Megillah 22a
Teaching one who has vowed renouncing benefit from him, or teaching his kids: Nedarim 35b, 36b-37a
Educators generally take a salary, and may take a salary, for teaching the Written Torah (specifically): Nedarim 36b-37a Taking pay for teaching how to read the Written Torah, or for guarding the schoolchildren: Nedarim 37a-b Honor of one who learned, but didn't teach: Megillah 28b
What happens if a teacher accidentally murders a student while disciplining him: Makkot 8a, 8b
Rav Acha removed a teacher for hitting the children too much, but Raveina returned him to his post because no one else could teach as well as he could: Makkot 16b Exiling a teacher to a city of refuge, if he is in the middle of teaching Torah: Makkot 10a
Advice for Education
Only a person who is expert in all areas of learning should teach publicly: Makkot 10a
One should only learn from a teacher who is pure: Moed Katan 17a
Teaching a student who doesn't behave well: Makkot 10a
Allowing the reading of a partial verse for education, because it is necessary: Taanit 27b
Beginning a Lesson with a joke: Pesachim 117a
One should teach [his child] out of a well-edited Book, because once an error is learned, it is hard to correct it: Pesachim 112a
One must teach with the briefest possible phraseology: Pesachim 3b
Care required to prevent students from mistaking actions for incorrect Law: Berachot 11a
Use of Mnemonics is important: Shabbat 104a
A teacher must be personally tough, but must teach gently: Taanit 4a
Related Laws
Requiring immersion for purification after emitting seed, before one may teach Torah: Berachot 22b
Beyond the Law
The translators of public Shabbat Classes will never see benefit from their salary, because it is so similar to Salary earned on Shabbat: Pesachim 50b
Learning Torah for the sake of Teaching it is termed "Torat Chesed [Torah of Generosity]": Succah 49b
One who teaches Torah to groups will, himself, gain a lot of Torah: Makkot 10a