General structural and complexity aspects

1. Relations between the ordinary and the odd crossing numbers.
2. An interesting connection - Sylvester's Four point problem.
3. Computational complexity hardness of determining the exact crossing number.
4. Fixed-parameter tractability of the crossing number problem.

Crossing-critical graphs

1. Definition of a critical graph, basic properties of critical graphs.
   
2. Overview of crossing-critical constructions; richness of critical graphs.
3. Deeper structural apsects and properties, and interesting questions.