Tomas Petricek and Jon Skeet have done a marvelous job of explaining functional programming in the simplest way possible: easing you in via a familiar language. Each chapter builds on the one before so that you gradually move from the simple and almost mundane to quite advanced techniques. Along the way, you clearly see the strengths of functional programming and .NET's new F# language. Unlike many tutorials, Functional Programming for the Real World breaks away from console-only math applications and delves into graphical and event-driven architectural problems.
In a recent Community for F# discussion, everyone noted that this is a fantastic resource for learning functional programming. Better still, it's a terrific resource for helping convince the rest of your team of the advantages of adopting a functional approach and F# as a language. I can think of few better reasons for getting this book immediately!