| Preface | p. IX |
| Introduction | p. 1 |
| The Riemann Zeta-Function and the Distribution of Prime Numbers | p. 1 |
| Bohr's Probabilistic Approach | p. 9 |
| Voronin's Universality Theorem | p. 12 |
| Dirichlet L-Functions and Joint Universality | p. 19 |
| L-Functions Associated with Newforms | p. 24 |
| The Linnik-Ibragimov Conjecture | p. 28 |
| Dirichlet Series and Polynomial Euler Products | p. 35 |
| General Theory of Dirichlet Series | p. 35 |
| A Class of Dirichlet Series: The Main Actors | p. 37 |
| Estimates for the Dirichlet Series Coefficients | p. 40 |
| The Mean-Square on Vertical Lines | p. 43 |
| Interlude: Results from Probability Theory | p. 49 |
| Weak Convergence of Probability Measures | p. 49 |
| Random Elements | p. 52 |
| Denjoy's Probabilistic Argument for Riemann's Hypothesis | p. 54 |
| Characteristic Functions and Fourier Transforms | p. 56 |
| Haar Measure and Characters | p. 57 |
| Random Processes and Ergodic Theory | p. 58 |
| The Space of Analytic Functions | p. 59 |
| Limit Theorems | p. 63 |
| Associated Random Elements and the Main Limit Theorem | p. 63 |
| Limit Theorems for Dirichlet Polynomials | p. 67 |
| An Ergodic Process | p. 70 |
| Approximation in the Mean | p. 73 |
| A Limit Theorem for Absolutely Convergent Series | p. 76 |
| Proof of the Main Limit Theorem | p. 80 |
| Generalizations | p. 83 |
| A Discrete Limit Theorem | p. 84 |
| Universality | p. 87 |
| Dense Sets in Hilbert Spaces | p. 87 |
| Application to the Space of Analytic Functions | p. 94 |
| Entire Functions of Exponential Type | p. 96 |
| The Positive-Density Method | p. 98 |
| The Support of the Limit Measure | p. 105 |
| The Universality Theorem | p. 106 |
| Discrete Universality | p. 109 |
| The Selberg Class | p. 111 |
| Definition and First Properties | p. 111 |
| Primitive Functions and the Selberg Conjectures | p. 116 |
| Non-Vanishing and Prime Number Theorems | p. 119 |
| Pair Correlation | p. 122 |
| The Phragmén-Lindelöf Principle | p. 124 |
| Universality in the Selberg Class | p. 128 |
| Lindelöf's Hypothesis | p. 130 |
| Symmetric Power L-Functions | p. 133 |
| Value-Distribution in the Complex Plane | p. 137 |
| Sums Over c-Values | p. 137 |
| Riemann-von Mangoldt-Type Formulae | p. 142 |
| Nevanlinna Theory | p. 147 |
| Uniqueness Theorems | p. 151 |
| The Riemann Hypothesis | p. 155 |
| Uniform Approximation and Zeros | p. 155 |
| Bagchi's Theorem | p. 156 |
| A Generalization | p. 160 |
| An Approach Towards Riemann's Hypothesis? | p. 162 |
| Further Equivalents of the Riemann Hypothesis | p. 163 |
| Effective Results | p. 167 |
| The Problem of Effectivity | p. 167 |
| Upper Bounds for the Density of Universality | p. 169 |
| Value-Distribution on Arithmetic Progressions | p. 174 |
| Making Universality Visible | p. 176 |
| Almost Periodicity in the Half-Plane of Absolute Convergence | p. 178 |
| Effective Inhomogeneous Diophantine Approximation | p. 182 |
| c-Values Revisited | p. 188 |
| Consequences of Universality | p. 193 |
| Dense Sets in the Complex Plane | p. 193 |
| Functional Independence | p. 195 |
| Joint Functional Independence | p. 198 |
| Andersson's Disproof of a Mean-Square Conjecture | p. 200 |
| Voronin's Theorems and Physics | p. 201 |
| Shifts of Universal Dirichlet Series | p. 202 |
| Dirichlet Series with Periodic Coefficients | p. 209 |
| Zero-Distribution | p. 209 |
| A Link to the Selberg Class | p. 216 |
| Strong Universality | p. 219 |
| Hurwitz Zeta-Functions | p. 223 |
| Joint Universality | p. 229 |
| A Joint Limit Theorem | p. 229 |
| A Transfer Theorem | p. 234 |
| Twisted L-Functions | p. 238 |
| First Applications | p. 245 |
| A Conjecture | p. 246 |
| L-Functions of Number Fields | p. 249 |
| Dedekind Zeta-Functions | p. 249 |
| Grössencharacters | p. 256 |
| Hecke L-Functions | p. 258 |
| Universality for Hecke L-Functions | p. 260 |
| Artin's Reciprocity Law | p. 261 |
| Artin L-Functions | p. 263 |
| The Artin Conjecture | p. 269 |
| Joint Universality for Artin L-Functions | p. 274 |
| L-Functions to Automorphic Representations | p. 278 |
| A Short History of Universality | p. 285 |
| References | p. 293 |
| Notations | p. 311 |
| Index | p. 315 |
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