$U$-projectors and fields of $U$-invariants

We present the general construction of the $U$-projector (the homomorphism of an algebra into its field of $U$-invariants identical on the subalgebra of $U$-invariants). It is shown how to apply the $U$-projector to find the systems of free generators of the fields of $U$-invariants for representations of reductive groups.