"Plates are plane structural elements with a small thickness compared to the planar dimensions. De-pending on the length to thickness ratios, plates are classified into moderately thick, thin and very thin plates. One of my primary research interests has been to employ finite element methods to determine approximations to deformation and stresses in thin and very thin plates when they are subject to loads. A Kirchoff model is used for the thin elastic plates and this leads to fourth order elliptic equations with the transverse displacement as the unknown variable. For very thin plates, a model proposed by von Kármán leads to a fourth order semi-linear system of partial differential equations with transverse displacement and stress variable as unknowns. My research work focusses on developing a priori and a posteriori error estimates for conforming, nonconforming, discontinuous Galerkin and mixed finite element approximations to fourth order elliptic equations and nonsingular solutions of von Kármán equations. Another area of interest is to study a priori and a posteriori finite element methods for distributed optimal control problems governed by thin and very thin plates."