Gemara

34b (Beraisa) Question: When is Bein ha'Shemashos?

Answer #1 (R. Yehudah): It is after sundown, as long as Penei Mizrach (the western sky) is reddish. When the horizon darkens, but not the middle of the sky, it is Bein ha'Shemashos. When the middle of the sky is as dark as the horizon, it is night;

Answer #2 (R. Nechemyah): It lasts the amount of time needed to walk (1000 Amos, i.e.) half a Mil after sunset. After this, it is night;

Answer #3 (R. Yosi): It lasts as long as the blink of an eye (a moment).

(Rabah): Bein ha'Shemashos lasts the time to walk three parts (quarters) of a Mil.

(Rav Yosef): It lasts the time to walk two parts (thirds) of a Mil.

35a (R. Yochanan): The Halachah follows R. Yehudah regarding Shabbos.

This is a stringency. (One must cease Melachah on Erev Shabbos once R. Yehudah's Shi'ur begins.)

(R. Yochanan): The Halachah follows R. Yosi regarding Terumah.

He does not permit to immerse during R. Yehudah's Bein ha'Shemashos (and eat Terumah at night). Since he forbids Melachah then, he considers it Safek! Rather, Kohanim may not eat Terumah until after Bein ha'Shemashos of R. Yosi.

Pesachim 92b (Mishnah): If one was Derech Rechokah (far from Yerushalayim) and did not bring Korban Pesach, he is exempt from Kares.

93b (Mishnah - R. Akiva): Derech Rechokah is further away than the city Modi'im.

(Ula): It is 15 Mil (a Mil is 2000 Amos, about a kilometer) from Modi'im to Yerushalayim;

(Rabah bar bar Chanah): An average person can walk 40 Mil in a day. He walks five Mil from dawn until sunrise, and five from sunset until Tzeis ha'Kochavim. This leaves 30 Mil from sunrise to sunset, 15 in the morning and 15 in the afternoon.

(Ula): Derech Rechokah is one who cannot reach the Azarah at the time of Shechitah.

Rishonim

Rif (15a): R. Yochanan rules like R. Yehudah regarding Shabbos. I do not know whether this is according to Rabah or Rav Yosef. We are stringent about Safek Isur. Also, the Halachah always follows Rabah against Rav Yosef, with only three exceptions. Therefore, from Sheki'ah the day is Kodesh, and one may not do Melachah.

Rosh (2:23): R. Yonah rejects this proof, for this rule applies only when Rabah and Rav Yosef argue about their own reasoning, for Rabah had stronger reasoning. Here they argue about what Rav Yehudah said!

Rambam (Hilchos Shabbos 5:4): From Sheki'ah until three medium stars are seen is called Bein ha'Shemashos.

Rambam (24:10): Anything forbidden due to Shevus, Chachamim did not decree about it Bein ha'Shemashos. They are forbidden on Shabbos itself, but permitted Bein ha'Shemashos for a Mitzvah or a great need. Therefore one may not tithe Vadai Tevel Bein ha'Shemashos.

Rosh (ibid.): Regarding Shabbos we do not light a Ner after Sheki'ah, like Rabah.

Terumas ha'Deshen (1): Some say Kri'as Shma three or four hours before Tzeis ha'Kochavim. There is no source to read so early. R. Tam said only from Plag ha'Minchah, i.e. one and a quarter hours before Tzeis ha'Kochavim. Some say that the hours are relative, based on 12 hours in a day. Even if the day is 18 hours, Plag ha'Minchah is less than two hours before Tzeis ha'Kochavim. Perhaps because people are weak, it is hard to wait until night to eat on the long days. Chachamim could not stop them. A Gadol said that in Krims they prayed and said Shma so early that after Seudas Shabbos they went to stroll by the river, and returned home before night

Tosfos (35b DH Hiksheh): Why did R. Yochanan need to say that regarding Terumah, the Halachah follows R. Yosi? He could have said that the Halachah follows R. Yehudah on Erev Shabbos, and R. Yosi on Motza'ei Shabbos! Or, he could have said that the Halachah follows R. Yehudah for Tevilah, and R. Yosi for eating Terumah! The Ri says that he prefers to teach that even regarding Shabbos, which is stringent, R. Yosi is lenient and permits Melachah during R. Yehudah's Bein ha'Shemashos. Even regarding Terumah, which is more lenient than Shabbos, or for Terumah mid'Rabanan, R. Yosi is stringent to forbid eating until his Bein ha'Shemashos finishes.

Yere'im (274; 102 in old editions): A Mishnah teaches that the entire day is Kosher for Shechitah. One who cannot reach the Azarah before Shki'ah is considered b'Derech Rechokah, and he is exempt from Kares. This shows that mid'Oraisa, the day ends at Shki'ah, which is five Mil before Tzeis ha'Kochavim.

Rebuttal (Gra OC 261 DH she'Hu): It is unreasonable to say that the horizon and sky get dark before sunset. Abaye looked (to see when it is dark). Beis Hillel permit several Melachos 'with the sun' (just before it sets).

Poskim

Shulchan Aruch (OC 261:1): Safek dark, i.e. Bein ha'Shemashos (Rema - the time to walk three quarters of a Mil after Sheki'ah) one may not tithe Vadai Tevel...

Shulchan Aruch (2): The beginning of Sheki'ah is when the sun goes below the horizon, until Bein ha'Shemashos, which begins three Mil and a quarter later.

Bach (2 DH Mihu): The Ra'avan argues with R. Tam. The Yere'im added that the three quarters of a Mil are before the sun sets. Once the sun disappears, it is total night mid'Oraisa, one and a half hours before the stars finish coming out. About a third of an hour before this is Bein ha'Shemashos. Hagahos Mordechai (2:456) and the Agudah (Shabbos 2:49) bring Ra'avan and the Yere'im, for they hold that one should be stringent like both of them for Torah Isurim. The custom is to be lenient like R. Tam and the Gedolim who agreed with him. One who is stringent like the Yere'im for the start of Shabbos will be blessed.

Bach: Surely, the custom in Krims (brought in Terumas ha'Deshen) was to pray so early because they held that the Yere'im's opinion is primary, and one must add from Chol to Kodesh. I saw many accept Shabbos two hours before night. Not only Chachamim and great people, rather, even proper Ba'alei Batim. Unfortunately, nowadays many are Mechalel Shabbos in fairs in Luvlin and Yarslav. We must stop this!

Magen Avraham (9): The Yere'im, Mordechai and Agudah say that Bein ha'Shemashos ends at sundown, and then it is night. Important people refrain from Melachah two hours before (Tzeis ha'Kochavim).

Gra: Bein ha'Shemashos is until the bottom horizon darkens, which is three quarters of a Mil in Bavel in Nisan or Tishrei. Shabbos 35b says that Tzeis ha'Kochavim (night) is when three medium-size stars can be seen. Experience testifies that this is long before four Mil after sunset. Rather, Bein ha'Shemashos starts immediately after sundown. Regarding Shabbos, we are stringent from the beginning of Sheki'ah. The same applies to Ner Chanukah. The Ran and Rashba say so, unlike the Tur and Shulchan Aruch. It is clear from R. Nechemyah's Shi'ur that Bein ha'Shemashos starts at Sheki'ah. After the time that one comes up from the sea, i.e. half a Mil, it is night.

Mishnah Berurah (23): One must refrain from Melachah from sundown. Happy is one who refrain from Melachah (or eating on Erev Yom Kipur) 30, or at least 20 minutes before sundown. This fulfills all the opinions (including the Yere'im), even if the time to walk a Mil is 24 minutes, and it fulfills many opinions regarding Tosefes Shabbos.

Bi'ur Halachah (DH mi'Tchilas): L'Chatchilah it is good to be stringent for the Re'em's opinion, even though the Gra rejected it.

Bi'ur Halachah (DH Kodem): Three medium stars is night for everything. Since we are not experts about what is medium, even R. Tam agree that one must refrain from Melachah three quarters of a Mil before any stars are seen. Minchas Kohen agrees. This is obvious. The Shi'ur of four Mil varies based on the latitude and time. In our lands, we often see stars before four Mil. Therefore, on Erev Shabbos one must refrain from Melachah before the time given in the Shulchan Aruch, even according to R. Tam, since it already became dark and it is night, or at least Safek night. Rather, one refrains at least half an hour (this includes Bein ha'Shemashos and Tosefes Shabbos) before when stars are normally seen. This is according to R. Tam. The Ge'onim obligate refraining from Melachah from Sheki'ah.

Kaf ha'Chayim (1): Ginas Veradim says that in all places people follow the Ge'onim. Our custom is to be stringent like the Ge'onim for the beginning of Shabbos or Yom Kipur.

Kaf ha'Chayim (331:36): If on a cloudy day people say that based on clocks the sun would be visible if not for the clouds, we rely on them. We are not concerned lest they err.

Bi'ur Halachah (DH v'Shi'ur): R. Yochanan was stringent about Shabbos and Terumah. Perhaps this is only because they are mid'Oraisa. Regarding Shevus (mid'Rabanan laws), even if Chachamim decreed Bein ha'Shemashos, perhaps this is only for R. Yosi's Bein ha'Shemashos. However, the Shulchan Aruch connotes that we are stringent also for the Shevusim of Sa'if 1. The Rema in Sa'if 1 holds like this, and Tosfos (35b) connotes like this (that we are stringent even for mid'Rabanan laws). The Rambam (24:5) forbids Shevusim Bein ha'Shemashos, i.e. from sunset.