In this talk, we will review classical methods to write down and to compute invariants of homogeneous forms. This will lead us to a short inspection of covariants and contravariants.

In a second part, I will explain how to use these technics for an efficient numerical computation of invariants.

We will apply this to the case of plane quartic curves. This will lead to a complete system of invariants.

Finally we inspect invariants for cubic surfaces. In this case we can compute invariants for a surface and we can construct surfaces with prescribed invariants.