The main interest of FGM lies on the possibility of tunning the stiffness properties of structural elements. Unlike layered materials, like sandwich structures, the possibiliy of delamination and debonding is an important drawback that can be solved by FGMs. This area of study is contanstly growing up and ca be faced from very different perspectives. I would say that it depends on which kind of materials are you interested in. For instance, if you are interested in nanocomposites, FGM nano-reinforced composites are studied from a multiscale perspective (atomistic models + micromechanical models + macroscopic models). My humble advise would be, first think of what kind of materials are you interested in, then, ask yourself, this material is apt for FGM applications. Then you could begin solving some specific problems like free vibration analysis of FGM plates. Here, it also depends upon which application are you interested in.