1. Introduction  
1.1 The dual problem of the GPM  
1.2 Atomic solution of the GPM  
1.3 GPM in terms of moments  
1.4 Inner and outer approximations  

2. Examples of GPM  

3. Semidefinite programming reformulations of the approximations  

4. Convergence results for the inner approximation hierarchy  
4.1 The special case of global polynomial optimization  
4.2 The general problem of moments (GPM)  

5. Convergence results for the outer approximations  
5.1 Asymptotic and finite convergence  
5.2 Error analysis for the case of polynomial optimization  

6. Concluding remarks