(Mishnah): One who builds his Sukah like a hut (the Schach leans against each other and serve as walls, like this ); or if he leans his Schach on a wall (like this ), thereby also using the Schach as the walls -

R. Eliezer says that it is invalid as it does not have a roof; Chachamim say that it is valid.

A large mat of reeds -

If it is made for lying on, it can contract Tumah and cannot be used as Schach.

If it is made as a covering, it can be used as Schach and it cannot contract Tumah.

R. Eliezer says - Whether it is large or small, if it was made for lying on it can contract Tumah and cannot be used as Schach; if it was made as a covering, it can be used as Schach and cannot contract Tumah.

(Gemara): R. Eliezer agrees that if the Schach was placed on four stones or was raised a Tefach above the ground, it is valid.

Beraisa: One who makes his Sukah like a House of the Forest of Levanon (like the house that King Shlomo built - see Melachim 1, 7, 3 - in which the roof was arranged in a zig-zag arrangement like this ), it is valid. (Note: This entry follows the understanding of Rav Chaim Kanievski.)

Question: For whom is this Beraisa needed?

Answer: For R. Eliezer (of the Mishnah, who holds that sloping tents are not considered tents, which is the reason that he disqualifies the cases at the beginning of the Mishnah. However, in this case there is a clear demarcation between the walls and the Schach, so although the Schach is irregularly shaped, it is valid.)

Aba bar bar Chanah quoting R. Yochanan: (The dispute in the Mishnah over mats) is about the mats of Usha (that are soft - the Tana Kama says that the large mats are usually used for coverings and R. Eliezer says that they are usually used for lying on).

R. Eliezer: Mats of Usha may be assumed to be Tameh unless they were made as tent coverings. Mats of Tiveria (are rigid and) may be assumed to be Tahor unless they were made for lying on.

R. Yitschak bar Chakulah and R. Shimon bar Rebbi ruled that the mats that are found hanging at the entrance of stores are Tahor (as they are not intended to lie on).

Query (R. Imi): May one use a weave that contracts Tumah (as it is used for lying on) as Schach?

Answer (R. Imi): It falls within the dispute of R. Eliezer and Chachamim.

R. Yitschak bar R. Elazar ruled in a case of great need that one may untie the ends of the mats and use the mats as Schach.

Question: Why did he only permit it in a case of great need? Since they no longer contract Tumah when the ends are untied, it should always be permitted to use them as Schach!