References on model checking and pi calculi
For the $\pi$-calculus, the following texts should be of interest. [1] is a relatively gentle introduction while [2] summarises the state of the art about 10 years ago. A lot  of progress has been made since, but that's not yet written up in a textbook. The original papers [3] are also quite readable but contain much detail that may overwhelm a novice (or may be instructive, since it's usually omitted in later accounts). Milner has written a little tutorial [4]. Finally, if you have not encountered process theory, the original CCS book [5] might be a good place to do so. It deals with CCS, a predecessor to the $\pi$ calculus, and key technical ideas in the theory of $\pi$-calculus like bisimulation are explained in a simpler setting.

Regarding the spi-calculus, I suggest to look at the original paper [6], but note that the spi-calculus has largely been superseded by the applied pi-calculus [7]. The applied pi-calculus is widely used in modelling cryptographic protocols. [8] is a tutorial of applied pi.


Communicating and Mobile Systems: The $\pi$ Calculus, by R. Milner.
The $\pi$-Calculus: A Theory of Mobile Processes, by D. Sangiorgi and D. Walker.
A Calculus of Mobile Processes, Part 1 and Part 2, by R. Milner, J. Parrow and D. Walker.
The Polyadic pi-Calculus: A Tutorial, by R. Milner.
Communication and Concurrency, by R. Milner.
A Calculus for Cryptographic Protocols The Spi Calculus, by M. Abadi and A. Gordon.
Mobile values, new names, and secure communication, by M. Abadi and C. Fournet.
Applied pi calculus, by M. Ryan and B. Smyth.


If you spell out the ideas you are looking for, maybe we can give you more focussed reading recommendations.