Annotation This advanced-level monograph addresses important problems in the calculus of variations by developing the basic lines of a general theory regarding integral representation, relaxation, and homogenization for unbounded functionals. Starting with an introduction to notation and an outline of the notions of convex analysis, the authors focus on homogenization issues, describing some asymptotic behavior results and reporting some surprising new phenomena related to the Lavrentiev gap. The techniques developed recover many of the results existing in the literature. The authors' approach is unified and elegant, the text well written, and the results intriguing and useful.