More than 30 measures of entropies have been introduced in the literature on Information theory generalizing Shannon's entropy. These are famous as parametric, trigonometric and weighted entropies. Rényi (1961)  for the first time gave the idea of parametric entropy. The idea of trigonometric entropies was initiated by Aczél and Daróczy (1963)  . Later Sharma and Taneja (1977) and Sant'anna and Taneja (1985)  studied it from different aspects. The idea of weighted entropies started by Belis and Guaisu (1968) . Later Picard (1979)  extended it for generalized measures. This chapter mainly deals with the parametric entropies involving one and two scalar parameters. After Rényi (1961) , other researchers viz., Havrda and Charvát (1967) , Arimoto (1971) , Sharma and Mittal (1975)  etc.. interested towards other kinds of expressions generalizing Shannon's entropy. Taneja (1989)  unified some of these. In this chapter, we shall study in details the idea of unification of different parametric entropies.