This talk is devoted to local normalization in some aspects of differential geometry and dynamical systems, which is a useful tool to study singularities.  

I will first recall some basic definitions in dynamical systems and the classification of nondegenerate singularities. 

Then I will introduce some classical results, including Poincaré-Birkhoff normal forms,  Poincaré-Dulac normal forms and the Siegel-Sternberg linearization theorem.

At last, I will briefly talk about my recent work with T. H. Minh and N. T. Zung on normalization of singular contact forms and primitive 1-forms.