This is the first of two books in the Calculus of Variations and Measure Theory where many results, some now classical and others at the forefront of research in the subject, are gathered in a unified, consistent way. Contemporary arguments are used throughout the text, streamlining well-known aspects of the theory, while providing novel contributions. The first book prepares the ground for the second in that it introduces and develops the basic tools in the Calculus of Variations and in Measure Theory needed to address fundamental questions in the treatment of functionals involving...