Translation:Shulchan Aruch/Orach Chaim/276

1. The Law when a Non-Jew lights a candle on Shabbos, having 5 Seifim: If a Gentile lit a candle for a Jew, it is forbidden for everyone, even for people it was not intended for. ''RAMA: It is immaterial whether a price was prearranged with him i.e. whether he was hired per lighting or per day, or was not hired, for since the Jew is benefiting from the Melacha (forbidden work) itself, it is forbidden under all circumstances. [Ha'gahos Ashiri, Beis Yosef in the name of the Smag]  However, if a Gentile lit for his own use or for a Jew who is ill, even if he is not life endangered,  RAMA: or for the sake of children, who have a status of an ill person not endangered [Mordechai] '', every Jew may make use of the candlelight. The same applies when a Gentile makes a bonfire for himself or for someone who is sick. Yet there are those that prohibit benefiting from a bonfire lest the Gentile add (to the fire) for him. '' RAMA: Nevertheless if a Gentile did it in a Jew’s house on his own accord, the Jew does not need to leave his house, even though he is benefiting from the candle or fire. [Tur] ''

2. When a Gentile lights a candle at an assembly of Jews and gentiles; if the majority present are gentiles one may benefit from the light of the candle, but if the majority present are Jews or even half-half, it is forbidden. If it is obvious that he lit it for a Gentile, for example – we see that the Gentile himself uses the light, even if a majority of Jews are present, it is permitted.  RAMA: Some authorities hold that it is permitted to ask a Gentile to light a candle in order to eat the Shabbos meal, as they hold that it is permitted to tell a Gentile to perform even a Melacha de’Oraissa (i.e. work prohibited from the Torah itself) for the sake of a mitzvah, [R"an in the name of the Itur] and accordingly many are accustomed to instruct a Gentile to light candles for a meal, especially for a wedding or circumcision meal, and nobody reprimands them. One should be stringent when not extremely necessary because most Poskim (religious decisors) disagree with this rule, see Siman 306. 

3. If one instructed a servant or maidservant to accompany him and they lit a candle to light the way, even though they also need it, it is not considered as being lit for their benefit since ultimately they are going along for the Jew. '' RAMA: It is permitted to tell a Gentile to accompany oneself with an already lit candle, because all that is being done is carrying the candle. (Rabbeinu Yerucham; Ha'Gahos Mordechai). ''

4. If there is a lit candle in a Jew’s house and a Gentile comes and lights another one, it is permitted to make use of its light as long as the first candle is burning, but after the first candle has gone out, it is forbidden to make use of the second candle. Also, if he added oil to an already burning lamp, it is permitted to make use of the light until the original oil has depleted, after that it is forbidden. '' RAMA: It is permitted to reproach a Gentile who is about to light a candle or add oil. (Tur) ''

5. It is permitted for a Gentile to make a fire in cold countries for children, and adults are permitted to warm themselves thereby. It is even permitted to make a fire for adults when it is extremely cold, as everyone is at risk of catching a cold. Unlike those that are accustomed to permit (lighting a fire) even when it is not an extremely cold day.