I've not seen this book myself, but if Steven Strogatz endorses it I figure it must be worth passing along:
Here's a promotional trailer for it:
It's also a course over at EdX:
Finally, there is an interesting review of the book in AMS Notices here:
It starts off somewhat negatively, and than wavers back-and-forth between positive and negative points, before concluding as follows:
"…'Street-Fighting Mathematics' is an engaging, well-written, insightful book. I do know that the book will provide any reader with new tools for making quick estimates and will introduce new ways of viewing problem solving. And I do know that I will read this book again. And again. And again. And maybe one day I will take the leap and actually use these methods to solve a problem."