TITLE: Graduate-level reference on temporal point processes
QUESTION [5 upvotes]: I am looking for a modern, graduate level, rigorous book on temporal point processes which also treats self-correcting point processes, and self-exciting point processes.
It would be even more interesting if the book was also pointing me to some research questions in the field.

REPLY [5 votes]: You can briefly read a short introduction to decide whether you are interested in the theoretic side or application side of the research subject. Say Rasmussen's Notes. 
If you are more interested in the theory, there is a two-volume standard text on theory of point processes. It includes a panoramic discussion on temporal/spatial process in Chap 14,15.

Daley, Daryl J., and David Vere-Jones. An introduction to the theory
  of point processes: volume I&II, 2ed, Springer, 2007.

If you are more interested in the application, there is a very popular book ABG discusses a variety of applications of point processes in survival analysis.

Aalen, Odd, Ornulf Borgan, and Hakon Gjessing. Survival and event
  history analysis: a process point of view. Springer Science & Business
  Media, 2008.