Shulchan Aruch Chapter 633:  The Laws of the Height of the Succah (10 Paragraphs)
Note: REMA in brackets

1.  A Succah that is greater than 20 cubits in height is invalid.  The same law applies whether it is big or small or if the walls touch the Sechach or don't touch the Sechach.  However, if the Succah is 20 cubits in height then it is valid.  Even if the walls of the Succah are greater than 20 cubits but the encompassing (roof) is within 20 cubits it is still valid.

2.  Suppose the Succah was higher than 20 cubits and one brings in material [he means small branches with their leaves] and builds a lower level of Sechach.  If the shade is greater than the sun then it is valid, but if not then it is invalid.

3.  A Succah who's contained (vertical) space was greater than 20 cubits and one hung nice things from the ceiling which go below 20 cubits, it is not considered a reduction.  Similarly, if one used vines and coverings it is not considered a reduction even if they "negate it" {1}.

4.  If one did reduction in size by adding straw and he negates the existing Sechach then it is considered a reduction.  Surely if one reduces it using earth (on the ground inside to make the Succah's height smaller) it is considered a reduction.  But other things are not considered a reduction until you reduce the height all the way to the opening..

5.  Suppose if the Succah was heigher than 20 cubits and one built a smaller enclosure opposite the center wall around the Succah. If the size is large enough to be a Kosher Succah then the whole Succah is valid even the part not under the enclosure.

6.  If one built this structure against a side wall, if the distance from the structure to a second wall is less than 4 cubits then it is valid but only the space inside the stucture.  If not then it is invalid.

7.  If one built this structure in the middle of the Succah, as long as there is 4 cubits or less between it and the surrounding walls.  The area inside the structure is valid even if it was higher than ten handbreaths.  But if there are not 4 cubits between it and the walls then it is invalid, even the area inside the structure itself.

8.  A succah that is not 10 handbreaths high is invalid.

9.  Ponder the case of a succah that is higher than 10 handbreaths but some branches from the Sechach reach below 10 handbreaths.  This is invalid even if these low reaching branches are the minority and the sun is would be greater than the shade from these few branches {2}.  However, if decorations reach below 10 handbreaths then they do not invalidate.

10. Supppose a Succah was less than 10 handbreaths high and someone sawed off from the Sechach enough material that it now contains10 handbreaths.  It is a valid Succah so long as there are 3 handbreaths betweeen the sawed off portion and the walls.  If not, it is invalid.

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{1}  I don't entirely understand what the end of his statement means.  I think he is saying that they perforate the Sechach above and make the previous Sechach small relative to the new material.  I will translate it this way from now on.
{2} Because it would be very difficult for a person to sit in such a small Succah (Mishna Brura)
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Shulchan Aruch Chapter 634:  A Succah Can Not be Less than Seven by Seven (4 Paragraphs)

1.  A Succah can that does not have an area of 7 by 7 handbreaths is invalid.  As far as the size of the walls, there is no maximum vertical height.

2.  If one is making a Succah in a wagon, one must be sure to have an area of 7x7 handbreaths.

3.  If the Succah had 7 by 7 handbreaths in size and one put garments inside for beauty that reduced the size to less than 7x7 handbreaths then it is invalid.

4.  If one ate a meal with his head and most of his body inside the Succah but with his table outside the Succah, it is as if he did not eat in the Succah.  This is true even if  one had a large Succah.  It is a Rabinnical decree ordained since we are worried that perhaps he will indadvertantly lean in the direction of his table.
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