R. Shimon Ben Gamliel was exceedingly modest and he said about his son Rebbe that he was a lion the son of a fox.
The Bnei Beseira were the Nesi'im in Eretz Yisrael and when Hillel arrived from Bavel they relinquished their position and appointed Hillel in their place.
Rebbe commented that afflictions are very great and he accepted upon himself thirteen years of affliction. (1)
The stable boy of Rebbe was richer that King Shvor.
A calf that was being taken to Shechitah and he went underneath the cloak of Rebbe and Rebbe said to it go because that was what you were created for and as punishment for not being merciful he was afflicted with Yisurin.
One time the maidservant of Rebbe was sweeping weasels out of the house and Rebbe told her to leaven them alone and subsequently his afflictions departed.
All of the years that R. Eliezer Bar Shimon suffered from afflictions nobody died before their time.
All of the years that Rebbe suffered from afflictions rain was not needed in the world and even though it did not rain when a radish was pulled from the ground the hole in the ground would fill with water. (2)
Rabah Bar Shila says that a rainy day is a difficult day just like a day of Din.
Anyone who teaches the son of his friend Torah will merit to sit in the Heavenly Yeshivah and anyone who teaches Torah to the son of an Am ha'Aretz even if Hashem Yisbarach makes a decree He will annul it for him.
R. Yochanan says if there are three generations of Talmidei Chachamim in the same family the Torah will never abandon the descendants of that family.
When R. Zeira ascended to Eretz Yisrael from Bavel he fasted for a hundred days so that he will forget the Talmud Bavli in order that it will not be a hindrance when he learns the Talmud Yerushalmi. (3)
R. Zeira also fasted for a hundred days so that R. Elazar will not die in his lifetime and he will be forced to take over the work of the Klal from him.
R. Zeira also fasted for 100 days so that he will not be burned in the fire of Gehinom.
The reason for the destruction of Eretz Yisrael was hidden from the Chachamim and the Nevi'im until Hashem Yisbarach explained that it was a result of the fact that they did not recite a blessing on the Torah. (4)
Anyone who lowers himself over Torah in this world will become great in the next world and anyone who makes himself a slave over the Torah in this world will become a free man in the next world.
The deeds of R. Chiya made it so that the Torah will not be forgotten from Klal Yisrael; he went from town to town and taught five children the written Torah and six children the Mishnah and instructed them to teach one another.
When R. Chiya and his sons prayed for rain when they said Mashiv ha'Ru'ach and the wind blew when they said Morid ha'Geshem the rain fell.
A BIT MORE
1. Rebbe saw that as a result of the afflictions of R. Eliezer Bar Shimon he merited that after he died his body remained intact and therefore he desired afflictions as well.
2. Rain is difficult for the world and if it was not needed in the world the Rabanim would pray that it will not rain and in the time of Rebbe rain was not needed at all and it didn't rain all of those years.
3. The Amora'im in Eretz Yisrael were not Ba'alei Machlokes and they learned without questions and answers and therefore the clarity of their learning was greater than that of Bavel.
4. Since they did not recite a blessing on the Torah they were demonstrating that they did not regard the Torah as an important gift.
When R. Zeira ascended to Eretz Yisrael from Bavel he fasted for 100 days so that he will forget the Talmud Bavli so that it will not be a hindrance when he learns the Talmud Yerushalmi. Rashi explains that the Amora'im in Eretz Yisrael were not Ba'alei Machlokes and they learned without questions and answers and therefore the clarity of their learning was greater than that of Bavel. The Maharsha asks that previously the Gemara stated that Reish Lakish asked R. Yochanan twenty four question on every statement that he made. The Maharsha answers that certainly in Eretz Yisrael the Amora'im also asked questions and gave answers however they did so only for the purpose of arriving at a greater understanding of the Gemara and eventually they reached clarity and a conclusion of the Halachah. In Bavel on the other hand they placed emphasis on Pilpul for the sake of Pilpul and not necessarily to arrive at greater clarity and therefore they did not always arrive at an agreed upon conclusion.
Just as it is a Mitzvah to teach Torah to a son it is also a Mitzvah to teach the son of a son and not only that but it is a Mitzvah for each Chacham of Yisrael to teach students who are also regarded as his children. However, a person should give preference to his son over his grandson and to a grandson over the son of his friend. A person is obligated to hire a Melamed (teacher) for his son but not for the son of his friend. (Shulchan Aruch YD 245:3, 4)
The Kesef Mishnah states that possibly one is also obligated to hire a Melamed for the son of his son and also for the grandson of his son. However, it is a Safek if the son of his daughter takes precedence to the son of his friend because maybe since he is not obligated to teach Torah to his daughter there is no special obligation to teach the son of his daughter. However I think that the son of his daughter has precedence over the son of his friend. (Shach)