Silting objects and t-structures in derived categories I,II,III Abstract: The notion of silting, generalising tilting, has been in the literature for over twenty years. Recent work by Aihara, Bondarko, Iyama, Keller, Koenig, Nicolas, Yang has shown deep connections of these objects with t-structures and co-t-structures in certain triangulated categories. In these talks we explore some of these connections and discuss important operations/constructions with silting objects, namely silting mutation and glueing with respect to a recollement. In the first talk, we will discuss the fundamental concept of t-structure. Certain collections of objects, ranging from simple-minded objects to ext-projectives in the aisle, will be discussed, as they parametrise suitable classes of t-structures in derived module categories. Moreover, we will recall an operation, namely the HRS-tilting, on t-structures. In the second talk, the connections between silting objects and structures in triangulated categories will be made explicit. Silting mutation will be introduced and compared with HRS-tilting. In the third talk, we will focus on glueing with respect to a recollement. Ranging from t-structures to co-t-structures, glueing techniques can be extended in a compatible way to silting objects. Moreover, we show that in the piecewise hereditary setting, all silting objects are obtained through this process.