Please note that within this document, the term "Tzitzit" refers to the fringe-strings which are worn on the corners of four-cornered garments.
Legal Issues
Defining the term, "Tzitzit": Menachot 41b, 42a
Whether the mitzvah is Person-Based, or Garment-Based: Shabbat 131a-b; Menachot 41a, 42b
Whether having strings on all of the four corners constitutes four separate Mitzvot, or they are all necessary to fulfill a single mitzvah: Menachot 37b-38a
Not travelling four cubits without Tzitzit: Shabbat 118b Performing the mitzvah with beautiful Tzitzit: Shabbat 133b
Whether kohanim are obligated: Menachot 43a
Whether women are obligated: Succah 11a [See Rashi "LePirzuma"]; Menachot 43a
Whether blind people are obligated: Zevachim 18b; Menachot 43a
When minors become obligated: Succah 42a
Whether avadim wear them: Menachot 43a
Putting them on a corpse before burial: Menachot 41a
Requiring that one separate the strings: Menachot 42a
The Tzitzit are items of a Mitzvah, not items of intrisic holiness, and so they may be disposed of after their Mitzvah is over: Megillah 26b