2. The book does not present every proof in details. Sometimes references are given, sometime just "left ot reader". You should check these out, even if, due to time constraints, you do not plan to give a full proof of every details. You should have an idea what lies behind the stuff that was swept under the rug. You may have to go back to earlier chapters of the book or to some other references (e.g. Rudin: Real and Complex analysis)
3. Don't get lost in the details, especially not at first reading. Always try to understand the essence first, even if it means simpler conditions or weaker result. Most mathematical proof consist of 10 percent essence and 90 percent technicalities, which can be learned along the way. Try to understand the 10 percent first.
4. Please use the blackboard and not projector.
5. The lecture should not go beyond the given time limit (about 60 minutes). Typically one can present much less than one thinks... Even if you happen to run out of time, make sure that the essential points are presented clearly, and you left out only technicalities.
6. If you have not held a public mathematical lecture yet, then it is a good idea to practice it. Go to an empty room with a board and just try to present the material loudly to yourself, or even better, if you can get a friend in the audience.
7. You can (even should) collaborate in understanding the material.
8. If you have questions (you should have!) do not hesitate to come either to me (room 329) or to my assistants: Heribert Zenk (room 334) or Dmitry Yarotsky (room 335). But you should not leave it to the last moment!
9. You should prepare a note for your presentation that you use during the lecture, but you should not simply read it. The note contains the basic formulas, computations, but not every word you will say. It serves as a reference and also a guideline for you during the talk. At least one week before your scheduled lecture you should show to us (either to me or Heribert or Dmitry) your notes. It can be handwritten, but it has to organized so that you can quickly find something in it if you get stuck.