Which is the best introduction to Kripkemodels for modal logics? I am a M.Sc in mathematics and know predicatlogic.

3$\begingroup$ The textbook on modal logic by Chagrov and Zakharyaschev, and the one by Blackburn, De Rijke, and Venema, contain a lot of introductory material on Kripke models, but neither is specifically focused on Kripke models. $\endgroup$ – Emil Jeřábek Sep 28 '16 at 9:08

$\begingroup$ You can see also an introductory exposition for Modal Logic into : James Garson, Modal Logic for Philosophers (2nd ed, 2013). $\endgroup$ – Mauro ALLEGRANZA Sep 29 '16 at 9:26

$\begingroup$ Reagrding Intuitionistic Logic, you can see ; Anne Troelstra & Dirk van Dalen, Constructivism in mathematics : An Introduction. Volume 1 (1988). $\endgroup$ – Mauro ALLEGRANZA Sep 29 '16 at 9:30

$\begingroup$ May also be useful : John Burgess, Philosophical logic (2009). $\endgroup$ – Mauro ALLEGRANZA Sep 29 '16 at 9:36

$\begingroup$ Maybe also Appendix A: Models of John Burgess, Kripke (2012). $\endgroup$ – Mauro ALLEGRANZA Sep 29 '16 at 9:41
Brian F. Chellas: Modal Logic: An Introduction, 1980.
Starts very basic but covers in detail the beautiful completeness theorem proofs for the basic systems like $S5$, $S4$, $K$.
I can't say that this is the 'best' introduction to Kripke models (as 'best' is always a relative term), but John P. Burgess's survey article "Kripke Models" presumes only knowledge of propositional and predicate logic. It can be found in Alan Berger (ed.), Saul Kripke, Cambridge University Press (2011), or on the Web at www.gauss.ececs.uc.edu/Courses/c626/reports.Kripke1.pdf . It covers most basic applications of Kripke models to modal logic adequately except for the application of Kripke models to forcing. A nice introduction to that topic might be the references in the comments and answer to the mathoverflow question, "Forcing is Intuitionistic". Also the Wikipedia entry, "Kripke Semantics".

$\begingroup$ Thank you for this reference, (the link worked fine) which seems to be to the point for me. $\endgroup$ – Anders Göransson Sep 29 '16 at 8:34

$\begingroup$ @AndersGöransson: Glad you found this reference helpful. The complete article is at www.gauss.ececs.uc.edu/.... , as referenced above. $\endgroup$ – Thomas Benjamin Sep 29 '16 at 11:39

$\begingroup$ I got the article downloaded straight away from the link you provided. It seems to cover all that I hoped for. $\endgroup$ – Anders Göransson Sep 30 '16 at 8:14