The current paper outlines a new algorithm, which is used to determine the exact solutions of ODEs and the similarity transformations of PDEs whose the invariant groups are known. Three groups of formulations (named by HAMAD Formulations) are presented: (I) Formulations for the exact solutions of ODE. (II) Formulations for similarity transformations of PDEs contains two independent variables. (III) Formulations for similarity transformations of PDEs contains three independent variables. By using these formulations enable readers can calculate the similarity transformations which transform PDEs to ODEs and also can calculate exact solutions of ODEs . Some examples are presented.