The first chapters of this book, written with Jean-Paul Dufour and published by Birkhauser in 2005, may serve as an introduction to Poisson geometry for interested people.
As regards normal forms, there are a number of interesting results which appeared in the literature after the publication of the book. In particular:
* The results by Cranic, Fernandes, Marcut, … (In particular, Crainic has a nice geometric proof of my local linearization theorem for proper Lie groupoids)
* The results by Stolovitch, Lorhmann, … (analytic/Gevrey local normal forms)
Comments welcome (especially about new developments)