Operads are algebraic structures formed by collections of operations p = p(x1,...,xn), where the number of variables n runs over N. Operads have been introduced in topology, in the sixties, in order to understand operations controlling associativity and commutativity defects in loop compositions. Since then, operads have been used in other domains fruitfully, and it has become clear that the notion of an operad provides a good conceptual and effective device to handle multiple structures in various contexts. We offered two courses on operads in 2012: a weekly course, at the Master degree level, from January until April 2012 in Lille, and a series of four lectures, at the Doctoral level, on May 15-22-29 and June 5, 2012, in Paris. The purpose of these courses is to explain new applications of operads. The courses are complementary, and as such, they can be followed together or independently. Both courses may also serve, at different levels, as an introduction to the theory of operads.