Compact Simple Lie Groups and Their $C$-, $S$-, and $E$-Transforms

New continuous group transforms, together with their discretization over a lattice of any density and admissible symmetry, are defined for a general compact simple Lie groups of rank $2\leq n<\infty$. Rank 1 transforms are known. Rank 2 exposition of $C$- and $S$-transforms is in the literature. The $E$-transforms appear here for the first time.