Topological modular forms / [edited by] Christopher L. Douglas...[et al.].

Includes bibliographical references.

Part I
1. Elliptic genera and elliptic cohomology by C. Redden--
2. Ellliptic curves and modular forms by C. Mautner--
3. The moduli stack of elliptic curves by A. Henriques--
4. The Landweber exact functor theorem by H. Hohnhold--
5. Sheaves in homotopy theory by C. L. Douglas--
6. Bousfield localization and the Hasse square by T. Bauer--
7. The local structure of the moduli stack of formal groups by J. Lurie--
8. Goerss-Hopkins obstruction theory by V. Angeltveit--
9. From spectra to stacks by M. Hopkins--
10. The string orientation by M. Hopkins--
11. The sheaf of E ring spectra by M. Hopkins--
12. The construction of tmf by M. Behrens--
13. The homotopy groups of tmf and of its localizations by A. Henriques--

Part II
Ellitpic curves and stable homotopy I by M. J. Hopkins and H. R. Miller--
From elliptic curves to homotopy theory by M. Hopkins and M. Mahowald
K(1)-local E ring spectra by M. J. Hopkins--
Glossary.

This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on elliptic curves and modular forms, a description of the moduli stack of elliptic curves, an explanation of the exact functor theorem for constructing cohomology theories, and an exploration of sheaves in stable homotopy theory. There follows a treatment of more specialized topics, including localization of spectra, the deformation theory of formal groups, and Goerss--Hopkins obstruction theory for multiplicative structures on spectra. The book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms.