Here are some suggestions to get you started.

Pi-Calculus

For a nice introductory survey, check out Joachim Parrow's contribution titled "An Introduction to Pi-Calculus" in the Handbook of Process Algebra, chapter 8. At a more involved level, the classic is Milner's own Communicating and Mobile Systems: The Pi Calculus, the tenth chapter of which presents two particular applications that you might be interested to hear about. If you can't get enough Pi from those, dig into Sangiorgi and Walker's The Pi-Calculus: A Theory of Mobile Processes.

Lambda-Calculus (typed)

There are so many introductory texts on this topic, it's hard to choose one. Just pick a popular programming language theory textbook (e.g., Pierce's Types and Programming Languages book) and there should be at least a chapter on typed lambda-calculus. At a more involved level, Hindley & Seldin's Lambda-Calculus and Combinators: An Introduction is a very accessible standard introduction to both lambda-calculus and combinatory logic. For all your other lambda-needs, Barendregt's The Lambda Calculus book is a classic, beastly volume, now available in an affordable paperback edition!

Note that there are many other accessible texts on both subjects, and lots of different learning paths you can take. For example, if you're already familiar with modal logic or game theory, there may be easier ways of getting introduced to Pi-Calculus and process algebras in general. You might also find it more enjoyable auditing (or enrolling in) a university course on concurrent processes or programming language theory.

Update: it appears that the question has changed (there was a lambda/pi typo!), so please ignore the stuff on typed Lambda-Calculus. I'm looking forward to hearing about typed Pi-Calculus.