Operads are mathematical devices that describe algebraic structures of many varieties and in various categories, where instead of studying the properties of a particular algebra, we focus on the universal operations that can be performed on the elements of any algebra of a given type. In this reading course, we will introduce the theory of algebraic operads and their properties, in particular the Koszul duality, and their applications to homotopical algebra. Students should seek the course instructor’s approval to take this course.