Whether telling a Gentile to do work for a Jew on Shabbat is Rabbinically prohibited: Shabbat 150a, 153a; Eruvin 67b-68a; Gittin 8b
If the Gentile does the work for his own benefit: Shabbat 121a, 122a-b
If the Gentile does the work for the Jew's benefit: Shabbat 122a-b
If the Gentile knows the Jew who benefits: Shabbat 122a
Giving an object found on Shabbat to a Gentile: Shabbat 153a
Candles do not require added work to benefit someone besides the lighter, and so he is benefitting others while he benefits himself: Shabbat 122a
Washing in a Shabbat-active bathhouse on Saturday night, in a town of Gentiles and Jews: Shabbat 122a, 151a
One may assume that work is done for the majority segment of town: Shabbat 122a-b
Gentiles helping one who is sick with a non-life-threatening disease: Shabbat 129a
Using an item which a Gentile brings from Outside of the Shabbat-Limit for Travel, for a Mitzvah: Shabbat 151a
Above, if it was from inside the Shabbat-Limit: Shabbat 151a
Above two cases, differentiating between where the work was done for the Gentile or for Jews: Shabbat 151a
Where it is not known whether the item had been outside of the Shabbat-Limit for Travel when Shabbat began: Shabbat 151a
Having a Gentile perform work for the sake of a Mitzvah: Eruvin 67b-68a
Having a Gentile perform work for the sake of a woman who has given birth: Eruvin 68a
