What are the Gemara's two sources for the basis of Eruv Tavshilin (Beitzah 15b)? What practical differences result?

How can the Rabbinical enactment of Eruv Tavshilin remove the Torah prohibition of preparing food on Yom Tov for after Yom Tov (albeit Shabbos)?

The Gemara (Yoma 28b) says that Avraham Avinu observed all of the Mitzvos, "and even Eruv Tavshilin!" Why do Chazal give this particular Mitzvah as an example?

According to Maharal, what is the deeper symbolism in Eruv Tavshilin?

What sort of food must be set aside as Eruv Tavshilin? Since the Halachah follows Beis Hillel that one cooked item is sufficient (Beitzah 15b, 17a), why do we set aside a baked item as well?

What foods do not qualify as the "cooked food" of Eruv Tavshilin? What food is recommended?

If one did not make a separate cooked item for Eruv Tavshilin, can he rely on a leftover part of another cooked item (which was not primarily for Shabbos)?

Why does Beis Shamai require setting aside two dishes?

What if one prepared, before Yom Tov, a cooked dish for Shabbos - but forgot to make the Berachah and declaration? What if one shortened the declaration, and did not specify the Melachos it should permit?

When the two days of Yom Tov (as observed nowadays in the Diaspora) fall on Thursday and Friday, and one forgot to make an Eruv Tavshilin on Erev Yom Tov, can one set aside a conditional Eruv on the first day of Yom Tov? Should the Berachah be recited?

When the Rav of a city makes his Eruv Tavshilin on behalf of the city, anyone who lives within the Techum may rely on it in case of need (Beitzah 16a). What about someone who lives outside the standard Techum, but can reach the city using his Eruv Techumin?

Must an Eruv Tavshilin that is being made on behalf of many people, contain a greater amount of food?

At what point on Yom Tov (Friday) should the Shabbos food be prepared?

[If one will not be cooking,] is an Eruv Tavshilin required in order to light candles on Yom Tov for Shabbos? Should a Berachah be recited on such an Eruv?

How long must the Eruv Tavshilin food remain? When is it customary to eat it?

What options for Shabbos food are available, for someone who is left without an Eruv Tavshilin?

If the purpose of Eruv Tavshilin is to ensure that we have sufficient food for Shabbos, why did the Sages impose a penalty on one who lacks an Eruv - leaving him without proper food for Shabbos!