Introduction .................................................. vii
1 Prologue ..................................................... 1
2 Irrationality I .............................................. 7
3 Irrationality II - Mahler's Method .......................... 20
4 Diophantine equations - Runge's Method ...................... 30
5 Irreducibility .............................................. 50
6 Elliptic curves - Stepanov's Method ......................... 64
7 Exponential sums ............................................ 76
8 Irrationality measures I - Mahler ........................... 88
9 Integer-valued entire functions I - Pуlya .................. 101
10 Integer-valued entire functions II - Gramain ............... 111
11 Transcendence I - Mahler ................................... 123
12 Irrationality measures II - Thue ........................... 133
13 Transcendence II - Hermite-Lindemann ....................... 158
14 Heights .................................................... 166
15 Equidistribution - Bilu .................................... 193
16 Height lower bounds - Dobrowolski .......................... 200
17 Height upper bounds ........................................ 212
18 Counting - Bombieri-Pila ................................... 218
19 Transcendence III - Gelfond-Schneider-Lang ................. 228
20 Elliptic functions ......................................... 243
21 Modular functions .......................................... 279
22 Algebraic independence ..................................... 292
Appendix: Neron's square root ................................. 312
References .................................................... 334
Index ......................................................... 342
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