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