Hadlakat Neir Shabbat

Rambam Mishna Torah, Hilchot Shabbat 30:1. Four things are said of Shabbat - 2 are from the Torah and 2 from the words of our sages and they were explained by the Prophets. In the Torah, it is written Shamor v'Zachor. And it was interpreted by the Prophets, Kavod v'Oneg. As it is written, (Isaiah 53:13) "...and you will call the Shabbat "oneg" to sanctify God, the honored (kavod) one."

Rambam Mishah Torah Hilchot Shabbat The lighting of Shabbat candles is not optional - i.e., if one wants to, he lights, and if one want to, he doesn't. And this isn't a mitzvah which one does not have to chase, such as Eruv Chatzerot or washing ones hand before eating - rather this is obligatory. And both men and women are obligated to have a candle lit in the home on Shabbat.

Midrash Tanchuma, Noach, siman 1 - It is written (Isaiah 58): "and you will call the Sabbath pleasurable (oneg)." This is the lighting of the candle on Shabbat.

Tosefot on "Lighting the candle is obligatory": Meaning, lighting it in the place of the meal is the obligation, that he should dine in the place of the candle because of "oneg" - enjoyment.

Rashi Shabbat 25b. Obligatory - it is Kavod Shabbos, that a meal is not special except in a place of light.

Rambam Mishnah Torah, Laws of Sabbath, 5:1

Even if he doesn't have what to eat, he borrows wicks and takes oil, nand light the candle, as this is part of Oneg Shabbat (pleasure of Shabbat). And one is obligated to make a blessing before the lighing: Baruch Atah Hashem Elokeinu Meleckh ha'olam asher....le'hadlik ner shel Shabbat - in the way that one blesses on all things which he is obligated from the words of our sages.

Rambam Mishnah Torah, Laws of Sabbath, 30:5 And one must prepare his house while it is still daytime becuase of Kavod Shabbos. And a light should be lit, and the table set for eating, and the bed should be made, as all these are in honor (kavod) of Shabbos.

Rashi on Shabbat 25b Lighting the Sabbath Candle: That he didn't have anything with which to light. And in a place where there is no candle, there is no "Shalom", that one walks and stumbles and walks in darkness.

Midrash Tanchuma, Parshat Noach

Our Rabbis have taught us that for several transgressions women die at the time of childbirth. So did our Rabbi teach on the 3...and the 3 are from the Torah. Nidah (laws of family purity)...(2) separation of Challah...and (3) lighting of the candle, as it is written Isaiah 58, "And you shall call the Sabbath oneg..." - this refers to the lighting of the Sabbath candle.

Custom of saying blessing for children at time of lighting...

Shabbat 23b

R. Huna said: He who habitually practices [the lighting of] the lamp will possess scholarly sons;

Compare language of bracha with number of candles lit...

Shulchan Aruch 263:1

One should be careful to use a nice candle/lamp, and there are those that prepare two wicks (lamps), one for Zachor, and one for Shamor. Rama: and one can add and light 3 or 4 candles, and so is the practice. The woman that forgets once to light, she lights 3 candles for the rest of her day, since one can add on the intended number, but not take away.