Gemara

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

(Rabah): This is forbidden even if it is the height of 10 houses!

20b (Beraisa): Before pitch the Mishnah lists Pasul wicks. Afterwards Pasul oils are listed.

Objection: This is obvious!

Answer: Wax was not obvious. One might have thought that it is Pasul even for a wick. The Beraisa teaches that this is not so.

Rishonim

Ba'al ha'Ma'or (8b): One might have thought that wax is Pasul also for a wick. The Gemara teaches that this is not so. I.e. it is Pasul only for oil, but it is Kosher for a wick. This is the source for lighting Neros Shabbos in which wax is like a wick. It is forbidden only if it is on a wick in a lamp of earthenware or metal, and the wax is like the oil.

Rebuttal (Milchamos Hash-m 8b): May one light a wick without oil?! Wax is Pasul for oil. It is clearly seen that they (wax candles) needs tilting and trimming more than an oil lamp. I needed to write this because the Rif forbids in a Teshuvah. There is no doubt about this.

Rashi (20b DH Sha'avah): One might have thought that a long "wick" of wax with a [standard] wick in it, like our candles, is Pasul. The Beraisa teaches teaches that this is not so.

Tosfos (20b DH Ad): Chachamim of Narvona permit a wick of wax in oil, but not a wax candle without oil. I say that if it were forbidden without oil, it would be forbidden even with oil, for below we forbid to wrap something we may light with around something we may not light with.

Hagahos Ashri (1:27): I am unsure whether one may not read by light of a wax candle, for there is no concern for tilting it.

Beis Yosef (OC 275 DH Kasuv): Surely it is forbidden, lest one trim and cut the end of the wick!

Tur (OC 680): Maharam says that his Rebbi, R. Shmuel, would put Ner Chanukah in the back of the door. Do not say that opening or closing the door brings the oil or wax closer to or further from the wick, so he burns or extinguishes. One may shake a table with a lamp on it so it will fall off. This shows that it is not burning or extinguishing. Even if it is, it is Davar she'Eino Miskaven. It is not a Pesik Reishei. The Ri forbids moving a door if a lamp is in it. He must say that one may shake a table with a lamp only if there is no oil in it. If it has oil it is a Pesik Reishei.

Poskim

Shulchan Aruch (OC 275:1): One may not read in a Sefer by light of a lamp, even if it is the height of 10 floors. Chachamim did not make distinctions. Therefore, we forbid even if it is in a lantern, and similarly a wax candle [is forbidden].

Taz (2): Do not say that the reason a wax candle is forbidden is because Chachamim do not distinguish. If so (it is not intrinsically forbidden), we would say that it was never forbidden! Rather, "and similarly" refers to the Reisha. (Wax candles are forbidden, just like a lamp.) Intrinsically they decreed about wax candles, lest one remove the end of the wick, which is extinguishing. The Beis Yosef says so, unlike those who were unsure about wax candles.

Suggestion: If so, on Yom Tov one may not read Piyutim by light of a lamp of wax candles, since extinguishing is forbidden even on Yom Tov!

Rejection (Taz): One extinguishes so that it will burn well. Just like one may burn on Yom Tov, one may extinguish slightly in order that it burn well. See 514:10. However, according to the Beis Yosef, why didn't the Gemara say so also regarding oil lamps, and we need not mention the concern for tilting? Tilting applies only when there is oil in the lamp, but if there is only a wick, it is permitted. According to the Beis Yosef, it is forbidden! Also, it seems that for a wax candle there is no Melachah for which one is liable mid'Oraisa. Even if he extinguishes, this is Melachah she'Einah Tzerichah l'Gufah. One is liable for extinguishing only if he does so to singe the wick (278:1)! Here, he merely removes an obstacle to burning, so he is exempt mid'Oraisa, and it is forbidden [mid'Rabanan]. Chachamim decreed lest one tilt only when there is concern for a Chiyuv mid'Oraisa!

Eliyahu Rabah (3): The Taz and Magen Avraham permit because even if he extinguishes through tilting, it is not an Isur Torah, for it is Melachah she'Einah Tzerichah l'Gufah, which most Poskim permit. However, in 514:10 we forbid cutting the end of the wick due to Tikun Mana (fixing a Kli). Malbushei Yom Tov 1) brings from the Tur (680) that there is concern for tilting. What the Beis Yosef brings from Hagahos Ashri is astounding. All the Acharonim say that there is no concern for tilting with wax candles. Also, the Tur (277) says that if one left a Ner on the table, he shakes the table and it falls, as long as it is a wax candle. This implies that tilting does not apply to wax candles. I say that the Tur in 680 discusses when one put wax in place of oil. Here we discuss wax wrapped around a wick. However, Milchamos Hash-m says that a wax candle needs tilting and trimming more than an oil lamp. This requires investigation. Also Maharshal connotes that tilting applies. Also, Milchamos Hash-m (45b) exempts Melachah she'Einah Tzerichah l'Gufah. If so, according to the Taz and Magen Avraham, why is there a decree lest one tilt? The Taz says that the Bach brings that Maharshal permits reading by light of a wax candle. This is wrong. He permits only for the Hagadah of Pesach. The Bach explicitly forbids reading other matters.

Mishbetzos Zahav: See Taz 514:12 and Magen Avraham 514:20. (One may not cut the wick with a Kli due to Tikun Mana.) The Beis Yosef did not say that it is due to extinguishing. He could hold that it is due to Tikun Mana!

Magen Avraham (3): Even though there is concern for trimming or cutting the end of the wick, like the Beis Yosef says, we can say that there is no Isur Torah. However, if there is no need, one should be stringent, for some say that extinguishing is a Melachah mid'Oraisa (334:27). Ra'avan is lenient about a lamp of Chelev, since it is repulsive.

Gra (DH v'Chen): There is concern for tilting also wax candles, like it says on 20b (according to Chachamei Narvona in Tosfos). Even according to Rashi [who permits a wax candle], there was a Hava Amina that one may not light with a wax candle, just like with Pasul wicks. The forbidden wicks and oils are due to concern for tilting! [This shows that tilting applies to wax candles - Damesek Eliezer. Therefore, any activity forbidden near lamps with Kosher oil is forbidden near wax candles.] Even according to the conclusion, we learn that it does not flicker, like oil.

Mishnah Berurah (3): Even if the candle is wrapped around the wick, like our candles of wax or Chelev, and there is no concern for tilting, there is concern lest he trim the top, and he extinguishes.

Mishnah Berurah (4): Also the Gra says that extinguishing applies to candles of wax and Chelev. Even so, I say that all permit to read by the light of our good Sterin (clear oil) lamps. The decree lest one tilt applies only to things that one sometimes tilts during the week, so it will burn nicely. One never needs to tilt a Sterin lamp. All the more so one need not trim [the wick], for its light is very clear and this is not needed at all.

Kaf ha'Chayim (12): The Magen Avraham (264:2) permits a Kosher lamp next to a Pasul lamp, i.e. only for matters that do not require scrutiny. What requires scrutiny is forbidden near a Kosher lamp, even if there is a wax candle near it.

Kaf ha'Chayim (11): Nesiv Chayim says that one should be lenient about wax candles only for the sake of learning. Ben Ish Chai permits this only if one cannot get a Shomer. One who fears Shamayim will lock the wax candle in glass and give the key to someone else, or tie it with an unusual knot, to fulfill the decree without question.

Bi'ur Halachah (DH v'Chen): If a candle of wax or Chelev is near an oil lamp, one may not read by the light. Even according to the Magen Avraham, who permits a Kosher lamp next to a Pasul lamp, it is forbidden, like the Pri Megadim says. However, one may read by light of a lamp next to a Sterin (clear oil) lamp.