Symplectic geometry — foundation

• Introduction to Symplectic and Hamiltonian Geometry — Ana Cannas, IMPA, Rio de Jeneiro '02

  Fastest intro to Symplectic Geometry, assuming basic Differential Geometry.

• Lectures on Symplectic Geometry — Ana Cannas, Springer Lecture Notes '06

  A much more detailed version of the previous one.

• Symplectic Geometry — Ana Cannas, Handbook of Differential Geometry '04

  More of a reference.

• Prerequisites from Differential Geometry — Ana Cannas, Handbook of Differential Geometry '04

The convexity theorem and symmetries

• Symplectic Toric Manifolds — Ana Cannas, CRM, Barcelona '01
• Convexity and Commuting Hamiltonians — Atiyah '82
• Convexity properties of the moment mapping — Guillemin, Sternberg '82

Quantization