I Principles and Qualitative Analysis.- 1. Absorption and Scattering of X-Rays.- 2. Characteristic Emission Spectra.- 3. Photoelectrons, Fluorescent Yields, and Auger Electrons.- 4. Qualitative Analysis.- 4.1. General Remarks.- 4.2. Anomalous Intensities of Lines in a Spectrum.- 5. Fluorescent Intensity of a Pure Element.- 5.1. Derivation of the Intensity Formula.- 5.2. Dependence of Fluorescent Intensity on the Anode Material of the Tube.- 6. Fluorescent Intensity of an Element in Two- and Multicomponent Mixtures.- 6.1. Derivation of the Intensity Formula.- 6.2. Intensity Formula for Low Concentrations.- 6.3. Effects of Associated Elements on the Fluorescent Intensity.- 6.4. Example for the Numerical Calculation and the Term Weighted-Average Wavelength.- 7. Interelemental or Secondary Excitation.- 8. Grain-Size and Surface Roughness Effects.- 8.1. Introduction.- 8.2. Homogeneous Powders.- 8.3. Heterogeneous Powders.- 8.4. Effects of Surface Roughness.- 9. Intensity Formula for a Divergent Primary Beam.- 10. Apparatus.- 10.1. Instrumentation of X-Ray Fluorescence Units.- 10.2. Generators.- 10.3. X-Ray Tubes.- 10.4. Spectrometers.- 10.5. Collimators.- 10.6. Crystals.- 10.7. Counters.- 10.8. Pulse-Height Analysis and Discrimination.- 10.9. Filters.- 11. Measurement Techniques.- 11.1. Principles of Statistics.- 11.2. Counting Statistics and Counting Loss.- 11.3. Background Correction.- 11.4. Optimal Conditions of Analysis.- 11.5. Short-Term Drift and Variations From Measurement to Measurement.- 11.6. Long-Term Drift.- 11.7. Errors Due to Sample Preparation and Calibration.- 11.8. Detection Limits.- II Quantitative Analysis.- 12. Calibration Curves and Regression Coefficients.- 13. Determination of Low Concentrations.- 13.1. Effects of the Matrix on Fluorescent Intensity.- 13.2. Quantitative Trace Element Determination.- 13.3. Use of Diffusely Scattered X-Ray Radiation.- 14. Determination of Thin Film Thicknesses.- 14.1. Determination of Mass Density.- 14.2. Semiquantitative Determination of Mass Density.- 14.3. Determination of Thin Film Thicknesses via Absorption.- 15. Determination of High Concentrations with Calibration Curves.- 15.1. Curves for Constant Admixture of a Third Component.- 15.2. Curves for Constant Mixing Ratios of Associated Components.- 15.3. Presentation in a Concentration Triangle.- 15.4. Correction for Effects of a Third Component by Correction Factors.- 16. Determination of Concentration, Formulated as a Linear System of Equations.- 16.1. Derivation of the Linear System of Equations.- 16.2. Formulation According to Sherman.- 16.3. Formulation According to Beattie and Brissey.- 16.4. System of Equations According to Marti.- 16.5. Formulation According to Traill and Lachance.- 16.6. Determination of the Interaction Coefficients.- 17. Analysis of Multicomponent Mixtures and Solutions for the Linear System of Equations.- 17.1. Separation into Subsystems.- 17.2. Decomposition and Dilution.- 17.3. Admixture of a Strongly Absorbing Substance.- 17.4. Internal Standard Method.- 17.5. External Standard Method.- 17.6. Double Dilution Method.- 17.7. Effects of Certain Minor Components.- 17.8. Semiquantitative Determination of Concentration.- 17.9. Direct Mathematical Solution.- 17.10. Mathematical Determination of Concentration of a Single Component in a Multicomponent Mixture.- 17.11. Appendix.- III Examples of Applications and Abstracts.- 18. Analysis of Mixtures Which Are Difficult to Separate Chemically.- 18.1. Zirconium-Hafnium.- 18.2. Niobium-Tantalum.- 18.3. Molybdenum-Tungsten.- 18.4. Scandium-Yttrium-Rare Earths.- 18.5. Thorium-Uranium-Plutonium.- 19. Steel and Iron Industry.- 19.1. Steel and Iron.- 19.2. Slags.- 20. Base Metals and Ores.- 20.1. Alloys and Industrial Materials.- 20.2. Ores.- 21. Light-Metal Industry.- 22. Determination of Thicknesses of Thin Films.- 23. Cement Industry and Silicate and Rock Chemistry.- 23.1. Cement and Clay.- 23.2. Silicates and Rocks.- 23.3. Determination of Coordination Number.- 24. Petroleum and Coal Industry.- 24.1. Trace Element Determination in Petroleum Products.- 24.2. Trace Element Determination in Catalysts.- 24.3. Determination of Admixtures in Fuels.- 24.4. Determination of Additives in Lubricating Oils.- 24.5. Trace Element Determination in Coals.- 25. Chemical Industry.- 25.1. Determination of Trace Elements.- 25.2. Determination of Major Elements.- 25.3. Determination of Organic Substances via X-Ray Analysis of an Associated Element.- 26. Medicine and Biology.- 26.1. Medicine.- 26.2. Analysis of Plants, Animal Feed, Water, and Air.- 27. Analysis of Small Amounts of Substance and of Small Areas.- Text References and Articles Abstracted in Part III.