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Covers ten lectures given by the author at the NSF-CBMS Regional Conference in the Mathematical Sciences on Deformation Theory of Algebras and Modules held at North Carolina State University, Raleigh, NC, May 16-20, 2011.

Bibliography

Includes bibliographical references and index.

Contents

Preface -- 1. Basic notations -- 2. Deformations and cohomology -- 3. Finer structures of cohomology -- 4. The gauge group -- 5. The simplicial Maurer-Cartan space -- 6. Strongly homotopy lie algebras -- 7. Homotopy invariance and quantization -- 8. Brief introduction to operads -- 9. L [infinity]-algebras governing deformations -- 10. Examples.