The case of an eruv that was set up on Shabbat intentionally/unintentionally and how it impacts one's ability to continue carrying within it

The teaching of Resh Lakesh that Avraham Avinu rescues any Jew from hell who has a circumcision, and the punishment of a Jew who has forbidden relations with a gentile

The aggadda of God creating man and woman as one creation and then splitting them, the source for 2 of the 7 berachot made at a wedding, the evils of not joining in the congregation's communal prayer

The laws of carrying when an eruv is dismantled or broken on Shabbat, do people need to be warned and told not to continue carrying in such a circumstance?

The case of building an eruv in the wilderness and why the Rabbis used the example of a caravan- was this an exclusive halacha or just the most typical case at the time- analysis of their principle that the Rabbis spoke contemporaneously

The principle of omed merubeh al haparutz (the solid sections of the fencing are greater than the breached/open sections) and the invalidation of an eiruv when an opening is more than 10 amot- application to the Seagate community Eruv

The rules of a lechi that is suspended above the ground more than 3 tefachim/handbreadths, machloket acharonim in the law of mechitza teluya

Analysis of the machloket Beit Shammai vs. Hillel, meaning of the phrase, "eilu v'eilu divrei elokim chaim"

How many walls are needed to permit carrying in a reshut hayachid? 3? 4? What constitutes a wall for this purpose?

Defining the parameters and power of the tzuras hapesach to transform a space into a private domain on Shabbat, application to laws of mezuza in different scenarios