Sukkot Section

The Brisker Rav, Yosef Ber, explain the name SIMCHAT TORAH as follows: Not only must we approach Torah with joy, but the Torah must also derive pleasure and joy from us. Hence the name Simchat Torah, literally, the joy of the Torah.

What & Where 
The Vilna Gaon points out that there are two mitzvot that a person fulfills with his whole self - Sukka and Eretz Yisrael. Both of these mitzvot are performed by "living", not just doing a specific act. One enters his Sukka and fulfills the mitzva. He makes Kiddush and HaMotzi and enjoys a sumptuous Yom Tov meal, and he continues to "get the mitzva". After Birkat HaMazon, he opens a sefer and learns in the Sukka and adds to the performance of the mitzva of Sukka After learning for a while, he plays a game of chess with his child in the Sukka and is still performing the mitzva.

Then he sits back in a comfortable chair and reads (a permitted) magazine article - and continues to fulfill the mitzva. And when he doses off and falls asleep, the person is still "getting" the mitzva. There is no other mitzva like this one. Except the mitzva of living in Eretz Yisrael. The Vilna Gaon cites the pasuk in T'hilim (76:3) as a "hint" to these two special, all-encompassing mitzvot. VAYEHI B'SHALEM" - What mitzvot are performed with "completeness"?, SUKO - the mitzva of Sukka, U'M'ONATO B'TZION - and when a person's place of residence is Eretz Yisrael. 
ASHREINU - happy and fortunate are we who are privileged to perform the mitzvot of Sukka and Yishuv Eretz Yisrael. 

Rain Check
Why are we exempt from Sukka if it rains? Should we not be required to perform the mitzva of Sukka with extra sacrifice, even in the rain? There are many examples of mitzvot that we are expected to go out of our way to perform. Even if it is inconvenient and difficult. Why are we not required to don rain gear and eat in the Sukka in the rain? 

The answer is based on the definition of the Mitzva of Sukka. IF the mitzva were to EAT or SIT in the Sukka, we would have to, even in the rain or other adverse conditions. But the mitzva is neither to EAT nor to SIT; it is the DWELL, to LIVE in the Sukka. Just as a person would not tolerate a leaking ceiling above his head in his own home, so too, we are not expected to live in the Sukka under adverse conditions. Add to the above the SIMCHA-factor of Sukkot. We cannot be commanded REJOICE and NOT be exempted in adverse condition.

And speaking of rain...
We say T'FILAT GESHEM on Sh'mini Atzeret, in Israel a.k.a. SIMCHAT TORAH. Most communities around the world say GESHEM as part of the beginning of the repetition of the Musaf Amida. Minhag Yerushalayim (followed by some shuls, not all, in Jerusalem) say GESHEM when the Torah's are being returned to the ARON KODESH just before the doors and Parochet are closed. 

T'FILAT GESHEM inaugurates the "mention" of G-d as "the One Who causes the wind to blow and the rain to fall" in our thrice (or four-times) Daily Amida. We start saying MASHIV HARU'ACH U'MORID HAGASHEM at Musaf of Sh'mini Atzeret (Simchat Torah). If T'FILAT GESHEM was said when the Torahs were being put away, then we need no special announcement by the Gabbai before the silent Musaf. Otherwise we get a loud "clop" and and announcement of MHUH.