Dynamical symmetries found in the nuclear structure physics are discussed.Based on these symmetries,several algebraic methods are explained and shown how powerful they are in order to predict nuclear excitation energies,and electro-magnetic properties.These algebraic methods are very essential to understand the nature of nuclear structure.Especially two models,the interacting boson model (IBM) and the pseudo spin scheme are discussed together with their microscopic interpretations.Finally their application,for example,to the molecular structure and quantum phase transitions are explained.My talk consists of the following section.