Book Recommendation for Poisson Manifold and Deformation Quantisation

Question

Can someone please recommend a basic introduction to the concept of Poisson Manifolds and Deformation Quantization. I'm new to Theoretical Physics and had to go through a lot of books before I even understood General Relativity. I found Hartle and A Most Incomprehensible Thing by Peter Collier to be easy enough books.

So are there any good texts that are simple enough?

P.S: I am well versed with Tensors, calculus, basic Quantum Mechanics and General Relativity. So, if I'm missing out on any topic that leads to Poisson Manifolds and Deformation Quantization, please point it out. Thanks!

Answer 1

A really nice book is

Poisson-Geometrie und Deformationsquantisierung: Eine Einführung (S. Waldmann).

It is a shame there is not an english translation. You could also check:

Lectures on the geometry of Poisson Manifolds (Izu Vaisman)

and for the connection with Lie groupoids/algebroids see:

Poisson structures and their normal forms (Jean-Paul Dufour).