In this shiur we dealt with the most important heter of amira l’nochri – b’makom mitzvah. This sugya is generated mostly from a gemara in Eruvin 67 and a question related to the existence of a single line in the manuscripts of the shas. Depending on how you read this sugya you could come up with one of three approaches:
1) Amira is permitted even when the action that the non-Jew is performing would be prohibited from the Torah, if it is for the sake of a mitzvah (Behag, Ittur).
2) Amira is permitted only when the action that the non-Jew is performing would otherwise be a rabbinic violation, if it is for the sake of a mitzvah (Rif, Rambam).
3) Amira is only permitted when the action that the non-Jew is performing would otherwise be a rabbinic violation – for the sake of the mitzvah of circumcision (Tosafot, Ramban).
You can see all the key mekorot here.
We also discussed the somewhat puzzling position of the Or Zarua that writing in a language other than Hebrew or Greek is only a rabbinic violation. This is one of the few instances in which the Aruch ha-Shulchan quotes the Mishna Berura.
You can see the Or Zarua at this link.
The shiur was broken up into three parts on the recorder.