The handouts for the course contain all the needed material but the following texts are good references.
1. Introduction to Mathematical Logic, Elliot Mendelson (https://www.karlin.mff.cuni.cz/~krajicek/mendelson.pdf)
2. A concise introduction to Mathematical Logic, W. Rautenberg (Springer 2006)
3. Elements of Finite Model Theory, L. Libkin (https://homepages.inf.ed.ac.uk/libkin/fmt/fmt.pdf)
4. Modal Logic, P. Blackburn, M. de Rijke, Y. Venema (Cambridge University Press)
5. Reasoning about Knowledge, R. Fagin, J. Halpern, Y. Moses, M. Vardi (MIT Press)
Some pointers to interesting general papers on Logic and CS:
Martin Davis, Influences of Mathematical Logic on Computer Science.
Martin Davis, Mathematical Logic and the Origins of Modern Computers.
Joseph Halpern, et al., On the Unusual Effectiveness of Logic in Computer Science.