I. Introduction 1
II. The Method of Moving Poles 3
1. Introductory Remarks 3
2. Derivation of the Fundamental Asymptotic Formula 4
3. Properties of the Elastic Scattering Amplitude at High Energies 7
4. Extension to Other Processes 9
5. Elastic π^-p Scattering and Contradiction Between Theory and Experiment 11
III. Theory of Peripheral Interactions 12
1. Initial Concepts and Formula for Total Cross Section 12
2. Classification of Methods 14
3. The Two-center Model 16
4. The Multiperipheral Model 20
5. Supplementary Remarks 24
IV. Experimental Data for E_L#app_gt# 10¹¹ eV. Comparison with Theory 24
1. Summary of Earlier Results 24
2. Methods of Experiment Analysis 25
3. Fundamental Experimental Results of Recent Years and Their Significance for the Theory 29
4. Conclusion 37
V. Connection Between the Method of Moving Poles with the Diagram Approach and the Onemeson Approximation 38
1. Formulation of the Problem 38
2. Diagram Interpretation of the MMP 38
3. Mixed Model 39
4. Inelastic Processes in the OMA and the MMP 41
Appendix 44
Cited References 46