Gemara

(Mishnah): One may not read by light of a lamp.

(Rabah): This is forbidden even if it is twice the height of an [average] person above the floor, or two even plowshare lengths above the floor, or even the height of 10 houses!

Inference: One person may not read, but two may. (One will remind the other if he goes to tilt it.)

Contradiction (Beraisa): It is forbidden for one or two people.

Resolution (R. Elazar): If they learning the same matter, it is permitted, but not if they learn different matters.

(Rav Huna): One may not read by light of a bonfire, even if there are 10 people.

(Rava): An important person may read by light of a lamp. (He normally does not tilt it even on a weekday.)

Question (Beraisa): Once, R. Yishmael ben Elisha was reading by light of a lamp, and was about to (some say that he actually did) tilt it.

Answer (R. Aba): We cannot learn from R. Yishmael. He would [waive his honor] and act like a commoner for the sake of Torah.

(Beraisa #1): A servant may check [the cleanliness of] cups and bowls by light of a lamp.

Contradiction (Beraisa #2): A servant may not check cups and bowls by light of a lamp.

Resolution #1: A regular [permanent] servant may not check. (He is concerned to check very well.) A temporary servant may check.

Resolution #2: Both refer to a regular servant. It is forbidden with an oil lamp, and permitted with a kerosene lamp. (It smells foul, so he will not tilt it.)

(Mishnah): However, a teacher... [he himself may not read].

Question: The Reisha permits him to see where they are reading;

Answer: He reviews only Roshei (the beginnings of the) Parshiyos. (He remembers the rest.)

Question: He may read the entire Parshah [just like children]!

(Beraisa - R. Shimon ben Gamliel): Children in the house of their Rebbi may arrange the Parshiyos and read by light of a lamp.

Answer #1: Also children may read only the beginning of the Parshiyos.

Answer #2: We are more lenient about children, for the fear of their Rebbi is on them.

Rishonim

Rashi (12b DH Roshei): The Chazan says the Roshei Parshiyos with his mouth. This suffices for him to remember everything tomorrow (at Kri'as ha'Torah)

Tosfos (13a DH Meisivei): Maharam says that according to Rashi, the Gemara did not ask from the Mishnah, for we could have said that the children read b'Isur, but we do not protest. The Beraisa connotes that it is l'Chatchilah.

Hagahos Ashri (1:31): The Chazan may read by light of a lamp and think in his heart, but he may not say the words. The entire Parshah is forbidden even to just think it.

Gra (DH v'Afilu): Obviously, anything that requires scrutiny is forbidden, even to distinguish between his and her clothes. We asked a contradiction from Beraisos about checking cups (and answered that a regular servant is forbidden, for he looks well, and will come to tilt. All the more so regarding learning - Damesek Eliezer.) We asked why the Seifa forbids reading, but the Reisha permits a teacher to see where the children are reading. (Damesek Eliezer - this shows that we do not distinguish reading from looking. If not, there was no question!) This is unlike Hagahos Ashri (who forbids saying even Roshei Parshiyos. Damesek Eliezer - really, there is no difference between looking, reading in his heart and saying the words. We permit Roshei Parshiyos, and forbid the entire Parshah.) Rashi explains that the Chazan says the Roshei Parshiyos with his mouth. This is not essential [to the answer]. Rather, he teaches that he may even say them with his mouth, lest we think that he may only look. A proof is from the question from R. Shimon ben Gamliel. One answer was that also children read only Roshei Parshiyos. (Surely, they read aloud!) This shows that one may read aloud.

Damesek Eliezer: We can answer for Hagahos Ashri based on Maharam in Tosfos. Hagahos Ashri can say that the Beraisa teaches that the Rebbi arranges the Parshah (in his heart) l'Chatchilah, and the children read [aloud] by themselves (b'Isur), but we do not protest. According to the second answer, they read l'Chatchilah.

Tosfos Yeshanim (21a DH Mipnei): Mahara (the Mordechai brings this in the name of Maharam) heard that if there is one Kosher lamp in the house, he will remember and not tilt other Neros in the room or cellar. R. Shimshon of Kutzi permits using any lamp for something one can do without a lamp, e.g. to take wine from a barrel.

Question: If there is daylight in a house, and there is a lamp in a dark part, may one read there by its light?

Answer (Hilchos Ketanos 2:27): R. Yishmael read and tilted, for he forgot that it is Shabbos. All the more so a commoner [must be concerned]! Light will not help in place of an Aveirah. Likewise, if there is a permitted lamp and a forbidden lamp, one may not read by light of the forbidden lamp.

Kaf ha'Chayim (275:14): Sha'ar Aryeh permits near Ner Shabbos, for it is different than lamps that burn during the week, so this is a Heker. Maharil Vavli questioned this, and the Birkei Yosef utterly rejected this.

Poskim

Shulchan Aruch (OC 275:1): One may not read in a Sefer by light of a lamp, even if he does not say the words with his mouth, lest he tilt [the lamp].

Magen Avraham (1): Likewise, one may not check Tzitzis [using light of a lamp].

Kaf ha'Chayim (3): One may not use light of a lamp with oils forbidden (for Ner Shabbos) even for matters that do not require scrutiny.

Shulchan Aruch (ibid.): This is even if it is the height of 10 floors, and he cannot reach it. Chachamim did not make distinctions. Therefore, we forbid even if it is in a lantern or in a hole in the wall.

Beis Yosef (DH v'Chasav): The Tur brings that Rabbeinu Peretz forbids even if it is in a lantern or in a hole in the wall. Semak says so.

Taz (1): Even though we find differences between one or two people, and many other distinctions below, those distinguish between different people. Some are permitted and some are forbidden. We do not decree about one person due to another. We do not find distinctions regarding the kind of lamp. Since there is an Isur when it is below, the Isur is not uprooted if it is elevated or closed in a lantern. Once it is forbidden, it is forbidden with the very Isur. This is unlike a person for whom it was never forbidden.

Bach (DH ul'Inyan, citing Maharshal): Nowadays people are lenient because they hold that only lamps (Kreizel) are forbidden. There is no concern for tilting with our candles. This is why the custom is to check Tzitzis by light of candles.

Magen Avraham (2): If the lantern is locked with a key, it is permitted. The Rosh, Maharam and their Talmidim did so, and so explain Hagahos Minhagim. The Bach (DH v'Achti) forbids.

Mishnah Berurah (2): If it is locked with a key, some permit. When it is 10 floors high, we forbid because this is normal. Sometimes a lamp is so high to enable seeing what is high. It is not normal at all to lock a lantern, if not for the Isur of Shabbos. This is a reminder. Surely he will not open it in order to tilt! This is like one who reads ba'Meh Madlikin (which discusses for which lamps we are concerned for tilting). Some forbid in every case, for do not distinguish. Eliyahu Rabah permits if he gave the key to someone else. This is like telling someone else 'pay attention to me, lest I tilt', which we permit (Sa'if 3). One may not read by light of a lamp during the day in a dark place.

Kaf ha'Chayim (6): The Bach and Taz forbid even if there is a key. Olas Tamid forbids even if he gave the key to someone else. Eliyahu Rabah and others permit in this case, but Machazik Berachah forbids. Shulchan Atzei Shitim permits to be lenient when there is a key only if there is a great need.

Kaf ha'Chayim (7): Machatzis ha'Shekel says that those who permit through a key, permit through an unusual knot. It is better than a key regarding sending things through Nochrim.

Bi'ur Halachah (DH l'Or): We do not use wax candles. Why are we lenient to read by light of a lamp? Meticulous people write in big letters on a piece of paper "today is Shabbos, and we may not light." Before Shabbos, they stick it on the handle used to move the wicks. Surely one may rely on this. This is no worse than being locked with a key or an unusual knot.

Kaf ha'Chayim (8): If light from a neighbor's house enters through a window or a hole in the wall, he may read by light of a lamp that comes through. One may not do so if the lamp is in another room of his house.

Kaf ha'Chayim (9): One may read Torah, Nevi'im and Kesuvim during the day on Erev Shabbos. We are not concerned lest he continue to learn at night, since learning at night is forbidden only due to a decree.

Kaf ha'Chayim (4): If one could read during the day without a lamp, he may read with a lamp.

Kaf ha'Chayim (8): If light from a neighbor's house enters through a window or a hole in the wall, he may read by light of a lamp that comes through. One may not do so if the lamp is in another room of his house.