Gemara

50b (Mishnah): Chavitim are kneaded, arranged (into loaves) and baked inside (the Azarah). All of these are Docheh (override) Shabbos.

Question: What is the source of this?

Answer (Rava): "Al Machavas" teaches that they must be cooked in a Kli Shares. The Kli is Mekadesh. If they were cooked the previous day, they would be Nifsalim due to Linah.

95b (R. Avahu bar Kahana): R. Yehudah and R. Shimon both expound "v'Hu Derech Chol Af Ki ha'Yom Yikdash ba'Kli." R. Yehudah says that David found Kohanim (in Nov) baking Lechem ha'Panim on Erev Shabbos, and corrected them;

Do you bake on a Chol day, even though it will become Mekudash in a Kli (the oven)? It will become Nifsal through Linah!

R. Shimon says, he found them baking it on Shabbos, and corrected them. 'You should bake on a Chol day (Erev Shabbos)! Do you think that the oven would be Mekadesh it, and it would be Nifsal through Linah? Only the Shulchan is Mekadesh!'

Shabbos 21a (Rav Huna): Oils and wicks that are Pasul (forbidden to use) for Ner Shabbos) are Pasul for Ner Chanukah, on a weekday and on Shabbos.

(Rava): Rav Huna holds that if it extinguished (the Ner extinguished), Zakuk Lah (one must relight it. He forbids Pasul wicks and oils on weekdays, lest the Ner extinguish and he will neglect to relight it). He permits using the light. (He forbids Pesulim on Shabbos, lest one use the light and come to fix the flame.)

(Rav Chisda): They are Kosher (for Ner Chanukah) on weekdays, but not on Shabbos.

He holds that if it extinguished, Ein Zakuk Lah (if it extinguished, he need not relight it). He permits using the light.

(Rav): They are Kosher for weekdays and Shabbos.

(R. Yirmeyah): He holds that if it extinguished, Ein Zakuk Lah; and he forbids using the light.

Abaye heard this in the name of R. Yirmeyah, but he did not accept it. He later heard that R. Yochanan said so, and accepted it.

Question (against Rav Chisda and Rav - Beraisa): The Mitzvah is for Ner Chanukah to burn from Shki'ah until the last people cease from the market.

Suggestion: If it extinguished, one must relight it!

Answer #1: No, this teaches that if one did not light at Shki'ah, he may still light until this time.

Answer #2: No, this teaches that one must put enough oil to burn until this time.

Pesachim 4b (Abaye) Question: There are two verses, "Shiv'as Yamim Se'or Lo Yimatzei b'Vateichem" (one may not own Chametz for any part of Pesach), and "Ach ba'Yom ha'Rishon Tashbisu Se'or mi'Bateichem"!

Resolution: Ha Keitzad (how do we resolve this)? "Ach ba'Yom ha'Rishon" refers to Erev Pesach.

Rishonim

Ran (Shabbos 9a DH Shma): If after lighting one came to fix it and accidentally extinguished it, the Rashba (1:539) said that presumably one need not relight it. This is like if it extinguished, Ein Zakuk Lah, for lighting is the Mitzvah, and he already lit it. If he relights it, he does not bless, for the Mitzvah already passed.

Terumas ha'Deshen (102): If Ner Chanukah extinguished on Erev Shabbos before he accepted Shabbos, it seems that he need not relight it. The Mordechai says that the Mitzvah begins from the end of Shki'ah, i.e. Tzeis ha'Kochavim but not before, for a Ner during the day does not help. If so the primary Mitzvah is not when he lights it during the day, rather, letting it continue to burn after dark. If so, we should say that if it extinguished, Zakuk Lah! However, we bless during the day '... v'Tzivanu Lehadlik Ner Chanukah', even though there is no Mitzvah yet! We must say that because there is no other possibility (to light at night on Shabbos), it is considered Hechsher (preparation for a) Mitzvah. Tosfos (Yevamos 6a DH she'Chen) says that if a father commanded 'slaughter or cook for me', there is no Mitzvah until the son feeds the father. Even so, there was a Hava Amina that this would be Docheh (Shabbos,) a Lav with Kares. This shows that fulfilling an Aseh through Hechsher Mitzvah is like the Mitzvah itself. Therefore, we bless on it. Also, if it extinguished, Ein Zakuk Lah, for the Mitzvah already began through Hechsher. A proof for this is that Rav permits Pasul wicks and oils on a weekday or Shabbos. The Gemara explains that he forbids using the light, and he holds that Ein Zakuk Lah. If he held Zakuk Lah, he would forbid Pasul wicks and oils, lest it extinguish and he will neglect to relight it. Rav Huna forbids Pasul wicks and oils, for he holds that Zakuk Lah. This proves that even in our case (Erev Shabbos), Ein Zakuk Lah. Rav permits Pesulim on Shabbos. He should be concerned lest it extinguish before Bein ha'Shemashos. According to the Mordechai, he did not yet do the Mitzvah! He cannot relight after accepting Shabbos, and all the more so Bein ha'Shemashos. He will lose the Mitzvah! There is more reason to decree about this than lest he be negligent and not relight it! Tosfos says that we decree lest it extinguish on Shabbos and he cannot relight it. Do not say that Chachamim were concerned lest it extinguish and he not relight it only when we are concerned for the entire time it must burn, but here the concern is only Bein ha'Shemashos before dark. If it extinguished after dark, Ein Zakuk Lah. This is a poor distinction. Ner Chanukah must burn half an hour after dark, and Bein ha'Shemashos is almost a quarter hour. If we are concerned lest it extinguish in half an hour, we should be concerned lest it extinguish in a quarter hour!

Question (Taz 673:9): Seemingly, if it extinguished, Ein Zakuk Lah applies after it burned after (the end of) Shki'ah. If one lit before this, and it extinguished before Shki'ah, surely Zakuk Lah. On Shabbos, one cannot light just before dark. One must light earlier. That time is called the beginning of the Mitzvah, just like on a weekday the end of Shki'ah is the Mitzvah. Chachamim enacted that one light when it is permitted. This is not mere Hechsher Mitzvah. It is truly the Mitzvah, like after Shki'ah (on a weekday). This is why on Shabbos one may light with Pesulim. If it extinguishes after Kabalas Shabbos, it is as if it extinguished on Shabbos. Indeed, if it extinguished before Kabalas Shabbos, one must relight it, even if he lit with good oil. Surely we do not learn what is possible (when he may still relight) from impossible (after Kabalas Shabbos). Chachamim permitted blessing before Kabalas Shabbos, but it is not yet truly Shabbos. Rav prayed Ma'ariv of Shabbos while it was day. Surely it did not become truly Shabbos to be liable for Melachah just like one is liable on Shabbos! The Beis Yosef (Sof 672, citing Mahari Avuhav) permits lighting from Plag ha'Minchah, just like one may pray Ma'ariv from then. Likewise, one may light and bless on Ner Shabbos from then, yet there is a Heter to do Melachah until Barchu. The same applies here. We should say that he was (Levushei Serad - not) Yotzei through it burning at that time. This is unlike Shechitah for one's father. He must slaughter in order to feed him. This is like after Kabalas Shabbos here. (One must light beforehand, so this is like the Mitzvah, but not if he can still relight it - PF.) Also Maharshal says that he should relight it, unlike the Terumas ha'Deshen. One should relight it if he did not yet accept Shabbos, but without a Berachah. The Rema calls this a stringency; I say that it is letter of the law.

Tosfos (51a DH Afi): Why do we say that if he baked Chavitim the previous day, they would be Nifsalim due to Linah? A Kli Shares is Mekadesh only in the proper time! Since it says "Al Machavas", this shows that it needs Kidush Kli. However, no verse mentions an oven for Shtei ha'Lechem. What is the source that baking them overrides Shabbos (according to R. Yehudah - 95b)? Since they are not Docheh Shabbos, Erev Shabbos is the time to bake them. (Since R. Yehudah holds that they must be baked inside, and it is the proper time, the oven is Mekadesh them - Yad Binyamin.) David rebuked the Kohanim based on their opinion that it must be baked on a weekday in a Kli Shares.

Emek ha'Melech (1:59 DH v'Al): Terumas ha'Deshen says that if Ner Chanukah extinguished before Kabalas Shabbos, Ein Zakuk Lah. Since he cannot light in the proper time, before Shabbos is like the proper time. This is like Tosfos in Menachos.

Tzlach (Pesachim 4b DH Amar): 'There are two verses' connotes that Abaye expounds an extra verse, like Tosfos explains. If he asked a contradiction, he should have said 'it says... and it says... , and he should have brought the verses in the order they are written. Rather, he brought "Ach ba'Yom ha'Rishon" last, for it is extra. ("Shiv'as Yamim..." is not extra. It forbids all seven days.)

Emek ha'Melech (1:59 DH v'Al): 'Ha Keitzad' connotes that Abaye comes to resolve a contradiction, like Rashi explains! According to Tosfos and the Terumas ha'Deshen, we should say that destroying Chametz just before Yom Tov is called ba'Yom ha'Rishon, since one cannot destroy it on Yom Tov! If so, there is no contradiction. What was Abaye's question? The Terumas ha'Deshen learned from Rav, who permits lighting on Shabbos with Pesulim. Initially, Abaye rejected R. Yirmeyah's Perush, and asked the contradiction in verses about Chametz. After he heard in the name of R. Yochanan and accepted the Perush, it was not a contradiction. Rather, he expounded an extra verse. This resolves Rashi and Tosfos, and the connotations of expounding an extra verse and of resolving a contradiction.

Poskim

Shulchan Aruch (OC 673:2): The Mitzvah is lighting. Therefore, if it extinguished before the time passed, Ein Zakuk Lah.

Taz (8): Why does Ein Zakuk Lah depend on whether lighting is the Mitzvah? Even if the Mitzvah is Hanachah (putting the Neros where they will stay), Ein Zakuk Lah! Also, the Gemara brought many proofs that we hold that Hanachah is not the Mitzvah. It did not prove this from this that we hold that Ein Zakuk Lah! Rather, the Shulchan Aruch does not mean 'because we hold that lighting is the Mitzvah, and not Hanachah..' Rather, once he lit, he already fulfilled the Mitzvah, therefore, if it extinguished, Ein Zakuk Lah.

Mishnah Berurah (25): If one saw that it did not light well and surely it will go out soon, he was not Yotzei, and letter of the law he must light again.

Bi'ur Halachah (DH Im): The greatest Hidur, to light one Ner for each day, applies at the time of lighting, so he must light all then. If one extinguished before lighting all of them, he must relight it. Ein Zakuk Lah applies even if all of them extinguished. The obligation to publicize the miracle is only at the time of lighting.

Shulchan Aruch (ibid.): This is even if it extinguished on Erev Shabbos before he accepted Shabbos, and it is still day.

Mishnah Berurah (27): If one accepted Shabbos and his Ner extinguished, if it is still before Shabbos, ha may tell a friend to relight it for him.

Shulchan Aruch (ibid.): Similarly, if after lighting he came to fix it and accidentally extinguished it, Ein Zakuk Lah.

Gra (DH v'Chen): Since we permit lighting with Pasul wicks and oils, this shows that also in this case Ein Zakuk Lah.Kaf ha'Chayim (55): If he extinguished it b'Mezid, he must relight it, but he does not bless.

Rema: If one wants to be stringent and relight it, he does not bless on this.

Taz (10): Maharshal says that one who wants the complete Mitzvah should relight it. This is no less than being Mehadrin. Shiltei ha'Giborim (9a:5) says that if one lit in a place of wind and it extinguished, he relights in a place without wind. It is as if he did not put in enough oil. I say that he does not bless again. Perhaps this is like using oils that are not drawn after the wick.

Kaf ha'Chayim (59): He may not relight it from another Ner Chanukah.

Note: One may relight it from the Shamash, or from any Ner after they burned the required time at night.

Kaf ha'Chayim (672:12): If one (lit before night on a weekday, and) put enough oil only for a half an hour, and it extinguished before night, he must relight it. However, in pressed circumstances one may light from Plag ha'Minchah, so perhaps he had enough oil, so he does not bless when relighting it. Chayei Adam says that if it does not burn at night, he was not Yotzei, so he blesses again. Since Poskim argue, he extinguishes it and lights again (with enough oil), but he does not bless again.