  We approach the cosmological inflation thought symmetries of differential
equations. We consider the general inflaton field in a homogeneous
Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime and with the use of
conformal transformations we are able to write the generic algebraic solution
for the field equations. We put emphasis on the inflationary models and we show
how we can construct new inflationary models from already known models by using
symmetry transformations.
