1/Quantum Theory and Gravitation.- 2/Quantum Mechanics and Classical Gravitation.- 2.1. Diffraction of Particles by a Grating.- 2.2. Diffraction of Particles by a Gravitational Grating.- 2.3. Gravitational Atomic Model.- 2.4. Equivalence Principle and Heisenberg's Fourth Relation.- 2.5. Quantum Mechanics and the Weak Principle of Equivalence.- 3/Measurement in Quantum Gravity.- 3.1. The Bohr-Rosenfeld Principles of Measurement in Quantum Field Theory.- (a) The Landau-Peierls Arguments.- (b) The Bohr-Rosenfeld Arguments.- 3.2. Measurement in Quantum Gravity.- 3.3. Ehrenfest's Theorems.- 4/Mathematical Descriptions of Quantum Gravity.- 4.1. Heisenberg-Euler-Kockel Approximation.- 4.2. On Gauge Fixing in Quantum Gravity.- 5/Quantum Postulates and the Strong Principle of Equivalence.- 5.1. Gravitons and the Linear Approximation of General Relativity Theory.- 5.2. Gravitons and the Nonlinear High-Frequency Approximation of General Relativity Theory.- 5.3. Compton Effect.- 5.4. Lamb Shift.- 5.5. Black-body Radiation.- 5.6. A Historical Remark: Black-body Radiation and Compton Effect.- 6/Planckions.- 6.1. Heavy Gravitons.- 6.2. Planckions as Biggest Elementary Particles and as Smallest Test Bodies.- 6.3. Foam and Block Spaces.- Appendix A/Massive Shell Models and Shock Waves in Gravitational Theories with Higher Derivatives.- Appendix B/On the Physical Meaning of Planck's 'Natural Units'.- References.