1. $\mathcal {F}$-spaces and $\mathcal {F}$-maps 2. $\mathcal {F}$-fibrations 3. $\mathcal {F}$-lifting functions 4. Categories of fibres 5. $\mathcal {F}$-quasifibrations and based fibres 6. Examples of categories of fibres 7. The geometric bar construction 8. Groups, homogeneous spaces, and Abelian monoids 9. The classification theorems 10. The definition and examples of $Y$-structures 11. The classification of $Y$-structures 12. A categorical generalization of the bar construction 13. The algebraic and geometric bar constructions 14. Transports and the Serre spectral sequence 15. The group completion theorem
