Review of the hardback: 'This text will serve as an admirable introduction to harmonic analysis as it appears in contemporary number theory and algebraic geometry.' Victor Snaith, Bulletin of the London Mathematical Society

• Part I. Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane: 1. Prerequisites and notation; 2. Review of SL2(R), differential operators, convolution; 3. Action of G on X, discrete subgroups of G, fundamental domains; 4. The unit disc model; Part II. Automorphic Forms and Cusp Forms: 5. Growth conditions, automorphic forms; 6. Poincare series; 7. Constant term:the fundamental estimate; 8. Finite dimensionality of the space of automorphic forms of a given type; 9. Convolution operators on cuspidal functions; Part III. Eisenstein Series: 10. Definition and convergence of Eisenstein series; 11. Analytic continuation of the Eisenstein series; 12. Eisenstein series and automorphic forms orthogonal to cusp forms; Part IV. Spectral Decomposition and Representations: 13.Spectral decomposition of L2(G\G)m with respect to C; 14. Generalities on representations of G; 15. Representations of SL2(R); 16. Spectral decomposition of L2(G\SL2(R)):the discrete spectrum; 17. Spectral decomposition of L2(G\SL2(R)): the continuous spectrum; 18. Concluding remarks.

Review of the hardback: 'This text will serve as an admirable introduction to harmonic analysis as it appears in contemporary number theory and algebraic geometry.' Victor Snaith, Bulletin of the London Mathematical Society

• Part I. Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane: 1. Prerequisites and notation; 2. Review of SL2(R), differential operators, convolution; 3. Action of G on X, discrete subgroups of G, fundamental domains; 4. The unit disc model; Part II. Automorphic Forms and Cusp Forms: 5. Growth conditions, automorphic forms; 6. Poincare series; 7. Constant term:the fundamental estimate; 8. Finite dimensionality of the space of automorphic forms of a given type; 9. Convolution operators on cuspidal functions; Part III. Eisenstein Series: 10. Definition and convergence of Eisenstein series; 11. Analytic continuation of the Eisenstein series; 12. Eisenstein series and automorphic forms orthogonal to cusp forms; Part IV. Spectral Decomposition and Representations: 13.Spectral decomposition of L2(G\G)m with respect to C; 14. Generalities on representations of G; 15. Representations of SL2(R); 16. Spectral decomposition of L2(G\SL2(R)):the discrete spectrum; 17. Spectral decomposition of L2(G\SL2(R)): the continuous spectrum; 18. Concluding remarks.

Review of the hardback: 'This text will serve as an admirable introduction to harmonic analysis as it appears in contemporary number theory and algebraic geometry.' Victor Snaith, Bulletin of the London Mathematical Society

• Part I. Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane: 1. Prerequisites and notation; 2. Review of SL2(R), differential operators, convolution; 3. Action of G on X, discrete subgroups of G, fundamental domains; 4. The unit disc model; Part II. Automorphic Forms and Cusp Forms: 5. Growth conditions, automorphic forms; 6. Poincare series; 7. Constant term:the fundamental estimate; 8. Finite dimensionality of the space of automorphic forms of a given type; 9. Convolution operators on cuspidal functions; Part III. Eisenstein Series: 10. Definition and convergence of Eisenstein series; 11. Analytic continuation of the Eisenstein series; 12. Eisenstein series and automorphic forms orthogonal to cusp forms; Part IV. Spectral Decomposition and Representations: 13.Spectral decomposition of L2(G\G)m with respect to C; 14. Generalities on representations of G; 15. Representations of SL2(R); 16. Spectral decomposition of L2(G\SL2(R)):the discrete spectrum; 17. Spectral decomposition of L2(G\SL2(R)): the continuous spectrum; 18. Concluding remarks.