Introduction.- Classical Diffeomorphism Invariance on the Worldline.- Quantum Diffeomorphism Invariance on the Worldline. The Relativistic Particle as an Archetypical Example.- Homogeneous Classical and Quantum Cosmology.- Weak-Coupling Expansion-. Quantum-Gravitational Effects in the Early Universe.- Conclusions and Outlook.- Appendix A Review of Gauge Systems and Constrained Dynamics.- Appendix B. The Traditional Born-Oppenheimer Approach to the Problem of Time.