The slides for this lecture review the notions of labelled transition systems, runs and traces, and give examples of the expansion of Petri net behaviour into labelled transition systems.
Boardwork then gave definitions of LTL formula, their meaning, and some small examples of application to LTS runs and Petri net behaviours.
Heiner et al. discuss how even finite reachability graphs for Petri nets may blow up very fast (§4(5)). However, they then jump straight to branching-time with CTL.
Huth and Ryan present the syntax and semantics of LTL (§3(2)) as well as some motivation on model checking.
The SPIN tool is based on LTL model checking.