Gemara

Version #1 (Reish Lakish): If one engages in Torah at night, Hash-m bestows grace on him during the day - "Yomam Yetzaveh Hash-m Chasdo uva'Laylah Shiro Imi";

Version #2 (Reish Lakish): If one engages in Torah in this world, which resembles night, Hash-m bestows grace on him in the world to come, which resembles day - "Yomam Yetzaveh Hash-m Chasdo...".

Sanhedrin 92a (R. Elazar): If Torah is not heard in a house at night, it will be burned - "...Te'achlehu Esh Lo Nupach Yera Sarid b'Ohalo";

Eruvin 65a (Rav Yehudah): Night was made for sleeping.

(Reish Lakish): Moonlight was created solely for Girsa (reciting teachings).

People told R. Zeira that his teachings are very clear.

(R. Zeira): I learned them during the day.

(Rav Nachman bar Yitzchak): We are like day laborers.

Ta'anis 31a: After the 15th of Av, one who increases (learning at night) will have increase (of years). If one does not increase, Ye'asef (his mother will bury him).

Avos 3:4 (R. Chanina bar Chachinai): One who is awake at night or travelling alone and diverts his mind to idleness is Chayav Misah (b'Yedei Shomayim).

Menachos 110a - Question: Why does it say "Avdei Hash-m ha'Omdim b'Veis Hash-m ba'Leilos"? (Avodah is primarily during the day!)

Answer (R. Yochanan): When Chachamim engage in Torah at night, it is considered as if they engage in Avodah.

Tamid 32b (Tana d'Vei R. Chiya): The Shechinah faces one who engages in Torah at night -- "Kumi Roni ba'Laylah... Nochach Penei Hash-m."

Bava Basra 20b (Mishnah): If Reuven set up a store in a Chatzer, others can stop him because the noise disturbs their sleep. They cannot complain if their sleep is disturbed by the noise of children

(Rava): The Seifa discusses one who teaches children Torah, after the enactment of Yehoshua ben Gamla.

Berachos 14a (Rav Acha): "V'Save'a Yalin Bal Yipaked Ra" - one who satiates himself with Divrei Torah before Linah (sleeping) will not receive bad tidings.

Rishonim

Rambam (Hilchos Talmud Torah 1:8): Everyone must fix times to learn Torah during the day and at night, even if he is old and weak, suffers from bodily afflictions, or must go begging for his food - "V'Hagisa Bo Yomam va'Laylah".

Rambam (2:2): We begin to teach children Torah at the age of six or seven. We teach them the entire day and a little at night, to accustom them to learning day and night.

Source #1 (Migdal Oz): He learns (the Chiyuv to learn at night) from Avos 3:4 and Ta'anis 31a.

Source #1 (Chasam Sofer CM 92 DH Lo): Bava Basra 20b says that neighbors cannot complain about loss of sleep due to children learning Torah. The Rambam infers that they learn at night. This is difficult, for a Beraisa (21a) forbids correspondingly to teach Nochri children. Surely they do not learn at night! Rather, some sleep during the day, e.g. children.

Source #3 (Gra YD 245 20): Ta'anis 31a says that if one does not increase learning at night after the 15th of Av, his mother will bury him. We say this only about a child.

Rambam (3:13): Even though it is a Mitzvah to learn day and night, a person learns most of his Torah only at night. Therefore, one who wants to merit the crown of Torah will be careful not to lose a single night with sleep, eating and drinking, conversation or similar things, only with Talmud Torah and Chachmah. The Goren (most texts - Rinah, exultation) of Torah is only at night - "Kumi Roni va'Laylah". If one engages in Torah at night, Hash-m bestows grace on him during the day - "Yomam Yetzaveh Hash-m Chasdo..." Any house in which Torah is not heard at night will be burned.

Tosfos (Eruvin 65a DH Ela): Night was made for sleeping, i.e. short summer nights.

Me'iri (Eruvin 65a DH Kol she'Mekaven): One should sleep at night so he can learn during the day without sleeping. Rav Nachman bar Yitzchak taught that we are like day laborers, i.e. we should strive to learn the entire day, for then we can get the most clarity.

Poskim

Shulchan Aruch (OC 238:1): One must be careful about learning Torah at night more than during the day. The punishment for neglecting to learn at night is greater (than for during the day).

Mishnah Berurah (1): Even in summer one must learn a bit before going to sleep.

Kaf ha'Chayim (3,4): The Zohar says that the primary learning should be after midnight. Nevertheless, one should learn before sleeping, like it says in Berachos 14a. The Magid urged the Beis Yosef to rise at midnight to learn, but also to learn Mishnayos before sleeping.

Bi'ur Halachah (155 DH Es): In addition to learning after Shacharis, one should learn between Minchah and Ma'ariv to fulfill the obligation of learning at night.

Shulchan Aruch (2): If one has a fixed amount to learn during the day and he was distracted and did not finish, he must finish it immediately at night.

Mishnah Berurah (5): This is because it is a Neder (Nedarim 8a), if he intended to do so always. One should stipulate from the beginning that it is not a Neder, lest it occur that he cannot fulfill it.

Mishnah Berurah (4): This applies even in short summer nights. He cannot compensate tomorrow, for tomorrow is its own Chiyuv.

Kaf ha'Chayim (8): Torah atones like Korbanos. At night we can finish Hakravah of Korbanos of that day. Likewise, we can complete the day's Torah at night.

Kaf ha'Chayim (9): It is proper not to sleep before three hours of the night. This includes the hour he prayed, and it suffices to begin the third hour. These hours should be spent learning.

Shulchan Aruch (YD 245:11): We teach children the entire day and a little at night, to accustom them to learning day and night.

Shulchan Aruch (246:1): One must fix times to learn Torah during the day and at night - "V'Hagisa Bo Yomam va'Laylah".

Pischei Teshuvah (2): Be'er Chayim says that judging or teaching children counts for this only if it is for free. He is unsure about one who learns fixed hours in Yeshiva and receives money for this.

Aruch ha'Shulchan (7): The simple meaning of the verse is to learn constantly. It also alludes to fixing times to learn, by day and at night, for the majority people who must spend time earning money.

Shulchan Aruch (23): One who wants to merit Keser Torah will be careful not to lose a single night with sleep, eating and drinking, conversation or similar things, only with Chachmah and Talmud Torah.

Rema: This is because a person learns most of his Torah only at night.

Prishah (54): "Yom l'Yom Yabi'a Omer v'Laylah l'Laylah Yechaveh Da'as" - during the day one says Divrei Torah to others, and at night he delves into them by himself.

Rema: One should start to learn at night from the 15th of Av and onwards (then the nights begin to get longer). One who does not increase (learning at night then) will perish.

Prishah (52): Tosfos (Eruvin 65a DH Ela) says that short summer nights are for sleeping, i.e. primarily for sleeping. One must learn somewhat. We say that long winter nights are for Girsa, i.e. primarily, but surely they are partially for sleeping!

Bach (OC 238 DH uva'Inyan): On Shavu'os we read in Megilas Rus "Shichvi Ad ha'Boker"; on Tish'ah b'Av we read in Eichah "Kumi Roni va'Laylah". This is a hint. From Shavu'os until Tish'ah b'Av the nights are short, so one may sleep until dawn. From Tish'ah b'Av until Shavu'os one must rise before dawn to learn.

Kaf ha'Chayim (5 and 1:10): The Zokar says that in all seasons one should get up at midnight for Tikun Chatzos. In summer he should go to sleep earlier. If he needs more sleep, he can sleep again after Tikun Chatzos until shortly before dawn, in order to join day and night through Torah and fulfill "A'ira ha'Shachar".

Magen Avraham (Reish OC`238): Some says that from the 15th of Av until the 15th of Iyar one must rise before dawn to learn. Some say that one may sleep eight hours, like the Gematriya of "Yoshanti Az Yani'ach Li." I say that it varies according to the person.

Mishnah Berurah (2): One should not sleep too much. Sleep is bad for Tzadikim (Sanhedrin 72a), for then they are not learning (Rashi).

Shulchan Aruch (24): Any house in which Torah is not heard at night will be burned.