Introduction

Conventions

1. Lie algebroids and Poisson geometry  
  1.1 Poisson manifolds  
  1.2 Lie algebroids  
  1.3 Gerstenhaber algebras and Batalin–Vilkovisky algebras  
  1.5 Lie bialgebroids  
  1.6 Lie algebroids with a Poisson structure  
  1.7 The big bracket  

2. The modular class of a Poisson manifold  
  2.1 Modular vector fields and modular class  
  2.2 Properties of modular vector fields  

3. The modular class of a Lie algebroid with a Poisson structure  

4. The modular class of a Lie algebroid  
  4.1 Lie algebroid representations  
  4.2 Characteristic class of a Lie algebroid representation in a line bundle  
  4.3 The modular class of a Lie algebroid  
  4.4 The case of Poisson manifolds  

5. The modular class of a Lie algebroid morphism  
  5.1 Lie algebroid morphisms  
  5.2 The modular class of a Lie algebroid with a Poisson structure revisited  
  5.3 Unimodularity  
  5.4 General morphisms of Lie algebroids  

6. The regular case and triangular Lie bialgebras  
  6.1 The regular case  
  6.2 Triangular Lie bialgebras  
  6.3 Frobenius Lie algebras  

7. The modular class of a twisted Poisson structure  
  7.1 Twisted Poisson structures  
  7.2 The modular class in the twisted case  
  7.3 The regular twisted case  
  7.4 Non-degenerate twisted Poisson structures  

8. Modular classes of Poisson–Nijenhuis structures  

9. The spinor approach to the modular class  

Conclusion