Preface and Acknowledgments viii
Introduction xi
Part I
1. Elliptic genera and elliptic cohomology
Corbett Redden 3
2. Elliptic curves and modular forms
Carl Mautner 17
3. The moduli stack of elliptic curves
e G. Henriques 25
4. The Landweber exact functor theorem
Henning Hohnhold 35
5. Sheaves in homotopy theory
Christopher L. Douglas 47
6. Bousfield localization and the Hasse square
Tilman Bauer 79
7. The local structure of the moduli stack of formal groups
Jacob Lurie 89
8. Goerss–Hopkins obstruction theory
Vigleik Angeltveit 93
9. From spectra to stacks
after Michael J. Hopkins 99
10. The string orientation
after Michael J. Hopkins 109
11. The sheaf of E∞-ring spectra
after Michael J. Hopkins 125
12. The construction of tmf
Mark Behrens 131
13. The homotopy groups of tmf and of its localizations
e G. Henriques 189
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