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1. Group structure. Preliminaries.- 2. Induced representations. Definition and various realizations.- 3. Further properties of the elementary representations.- 4. Intertwining operators: X-space realization.- 5. Momentum space expansion of the intertwining distribution and positivity.- 6. Nondecomposable representations and intertwining differential operators.- 7. Discrete and general properties of the discrete series.- 8. The Plancheral theorem. Concluding remarks.- 9. The Kronecker product of two elementary representations.- 10. Construction of the Clebsch Gordan expansion.- 11. Special cases and further properties of the expansion formula.- 12. Renormalizable models of self-interacting scalar fields. Dynamical equations for Green functions.- 13. Invariance and invariant solutions of the dynamical equations. Conformal partial wave expansion for the Euclidean Green functions.- 14. Implications of the dynamical equations. Pole structure of conformal partial waves.- 15. Another form of the conformal expansion, involving a Minkowski momentum space integral. The Q-kernels.- 16. The problem of crossing symmetry. Concluding remarks.