The importance of similarity transformations and their applications to
partial differential equations is discussed. The theory has been pres
ented in a simple manner so that it would be beneficial at the undergr
aduate level. Special group transformations useful for producing simil
arity solutions are investigated. Scaling, translation, and the spiral
group of transformations are applied to well-known problems in mathem
atical physics, such as the boundary layer equations, the wave equatio
n, and the heat conduction equation. Finally, a new transformation inc
luding the mentioned transformations as its special cases is also prop
osed.