(Mishnah): A stolen or dry Esrog is invalid.

If it came from a tree that was worshipped as an idol or from a city that must be destroyed (due to the idol worship that exists there), it is invalid.

If it is Orlah (a fruit that grows within the first three years of the life of a tree) it is invalid. If it Terumah Temeyah it is invalid. If it is Terumah Tehorah he should not take it, but if he did, it is valid.

If it is Demai, Beis Shamai say that it is invalid and Beis Hilel say that it is valid.

If it is Maaser Sheni in Yerushalayim, he should not take it, but if he did, it is valid.

(Gemara): The Pasuk states (Vayikra 23, 40), "...[you should take for yourselves]...a fruit of the 'Hadar' tree". A tree that both its fruit and its branch is beautiful - this is the Esrog tree.

If you suggest that it is the Pomegranate tree, its fruit is beautiful but its branch is not.

If you suggest that it is the Carob tree, its branch is beautiful but its fruit is not.

Only the Esrog tree has both of these characteristics.

"Hadar" - R. Levi expounds - a fruit that stays (Dar) on the tree from year to year.

R. Tanchuma: Akilas translated Hadar to be "Hidur" (Greek for water) - a tree that grows from all types of water (e.g. rain/irrigation/spring).

Beraisa (R. Shimon B"Y): The Pasuk states (ibid), "You shall take for yourselves a fruit of the Hadar tree" - a tree that both its fruit and its branch is beautiful; the fruit tastes like the branch; the branch tastes like the fruit; its fruit is like its branch and its branch is like its fruit - this refers to the Esrog tree.

R. Yaakov Daromaya: The end of our Mishnah does not follow Beis Shamai, as it first teaches that according to Beis Shamai, an Esrog of Damai is invalid. (The assumed reason is that the Esrog will become Muchshar (prepared) to receive Tumah when it comes in contact with the wet Lulav - since it is prohibited to cause the Terumas Maaser and Maaser Sheni inside it to become Tameh, Beis Shamai prohibit using such an Esrog). Beis Shamai is unlike the end of our Mishnah that teaches that one should not take an Esrog of Maaser Sheni in Yerushalayim, but if he did, it is valid. (Beis Shamai should have said such an Esrog is completely invalid.)

(Mishnah): If bumps developed on most of it, its Pitam was removed, it was peeled, it was split or it had a hole and was lacking, in all of these cases it is invalid.

If bumps appeared on only part of it, its Ukatz was removed or it had a hole but was not lacking anything, in all of these cases it is valid.

A Kushi (black) Esrog is invalid.

An Esrog that is green like a leek -

R' Meir says that it is valid.

R' Yehudah says that it is invalid.

(Gemara - R. Yitschak bar Nachman quoting Shmuel): All of the disqualifications of the Mishnah only apply on the first day of Sukos.

When the Mishnah taught that bumps on most of it is invalid, we are referring to most of one side, but if it is in two or three places then even on bumps on part of it would be invalid.

If bumps appear on the 'nose', i.e. on the wider part near the top, before it slopes towards the top, it is considered as if there are bumps on most of it and it is invalid (because it is more visible).

The Mishnah had taught: If its Pitam was removed...it is invalid.

In Bavel they say that the Pitam refers to the "flower" on top of the "nipple" which protrudes from the top of the Esrog. (Even if only the "flower" was removed but the "nipple" part remained, it is still invalid.)

R. Yitschak bar Chakula: It is the "Pika" - the end of the branch which enters the bottom of the Esrog, where it hangs from the tree.