1) AGADAH: "ULAH/OLAH SHEL TESHUVAH"
OPINIONS: The Gemara quotes the verse, "[These are the last words of David,] the word of David, son of Yishai, and the word the man who was set up on high (Al)" (Shmuel II 23:1). The Gemara reads the word "Al" ("on high") as "Ol," and it derives from the verse that David ha'Melech raised the "Ol" of Teshuvah. What exactly does the Gemara mean?
(a) RASHI in the Ein Yakov (Moed Katan 16b) explains that "Ol" means purpose. The RIF in the Ein Yakov there explains that David ha'Melech established Teshuvah as a goal among the Jewish people. The Gemara here earlier explains that David's repentance showed that even when one is not part of a Tzibur (on whom Hash-m has more mercy) his Teshuvah still is accepted. This "raised" the "purpose" of Teshuvah among the Jewish people and showed them that even an individual's repentance is accepted by Hash-m.
(b) The TORAS CHAIM explains that raising the "Ol" means that David ha'Melech accepted upon himself the yoke ("Ol"), or burden, of having to do Teshuvah for his sins. The IYUN YAKOV gives a similar explanation and notes that David accepted upon himself six months of affliction in order to atone for his sins (see Sanhedrin 107a).
RAV YITZCHAK HUTNER zt'l (in PACHAD YITZCHAK, Yom ha'Kipurim 11:6) gives a similar explanation. He adds that the acceptance of the yoke of Teshuvah is not merely a personal matter. Rather, it is a communal matter, because the coming of Mashi'ach depends on whether the people are righteous or not. David ha'Melech realized that he had to accept the yoke of Teshuvah not just for himself but for the benefit of the entire nation.
(c) The MAHARSHA explains that there is another meaning to the word "Ol." The word "Ol" refers to a Korban Olah, which atones for sinful thoughts. The Gemara teaches that David ha'Melech did not actually sin when he married Bas Sheva, since her husband, Uriyah, had given her a conditional Get (see Shabbos 56a). However, if Uriyah would not have come back it seems that he would have transgressed this prohibition. Since David put himself in a situation in which he might become guilty of committing a sin, he needed to repent, the type of repentance attained by offering a Korban Olah which atones for sinful thoughts.
(d) Rav Hutner (Pachad Yitzchak, Yom ha'Kipurim 11:3) quotes the VILNA GA'ON who relates the word "Ol" to the word "Aliyah." Rav Hutner explains that the Vilna Ga'on means that although David ha'Melech experienced a decline in his spirituality as a result of the incident with Bas Sheva, he accomplished an "Aliyah Shel Teshuvah," raising himself through Teshuvah to his previous status. (Y. MONTROSE)
2) AGADAH: MAN AND TORAH: LIKE AN OX TO HIS YOKE, LIKE A DONKEY TO HIS LOAD
OPINIONS: The Gemara teaches that a person should always fasten himself to words of Torah like an ox is fastened to his yoke and like a donkey to his load. Why does Gemara compare a person's acceptance of the yoke of Torah specifically to the yoke of oxen and donkeys?
(a) The BEN YEHOYADA explains that the Gemara is teaching that a person must learn Torah whenever possible. Those who do not learn Torah will meet one of two fates. One is that of an ox that always carries its yoke, and one day acts sick and stops carrying its yoke. The owner will slaughter the ox in order to at least benefit from the meat. Similarly, a person who stops learning Torah altogether separates himself from his source of life, the Torah. The second fate is that of a person who learns Torah, but does so lazily, without exerting sufficient effort. His fate is that of a donkey. A donkey is not in danger of being eaten, since its meat is not kosher. However, if a donkey acts lazily, its owner will hit it to make it move faster. Similarly, a person who learns Torah lazily will suffer from Yisurim (afflictions).
(b) The SHEM MI'SHMUEL (Tzav u'Parah 5679) explains that an ox and donkey have two distinctly different traits. Although an ox appears to be a proud animal and is adorned with horns, it still accepts a yoke upon itself and goes to work. A donkey is a lowly animal, but it, too, accepts its work happily. Similarly, a person should realize that he must have these two traits when he learns Torah. These animals are examples of the work ethic which a person should apply to his learning.
(c) The CHAFETZ CHAIM (in SHEM OLAM #10) explains that an ox and a donkey perform two different types of work. An ox plows a field and prepares it for planting. A donkey carries the grain once it is harvested. Similarly, a person who learns Torah must have both the ability to analyze a Sugya and prepare the material in a way in which it will produce "fruit" -- a clear understanding of Torah. Once he has attained this understanding, he must do the work of the donkey; he must constantly carry his Torah with him by reviewing what he has learned. The Chafetz Chaim points out that the Gemara uses the word "always" in order to emphasize that this is the method which one should use in every Sugya that he learns. A person should not think that people from previous generations have already done all of the work in the "field," leaving no potentially new crops. A person always has the ability to reveal new insights in Torah, even in Sugyas which have been learned by great Talmidei Chachamim throughout the generations. (Y. MONTROSE)