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Hilbert’s Fourteenth Problem asks if certain k-algebras areÌýfinitely generated. We will look at this problem from the point ofÌýview of Geometric Invariant Theory: Say a group G acts on an affineÌývariety X. Then we can ask whether the subring of G-invariants of theÌýcoordinate ring k[X] is finitely generated. Hilbert showed that thisÌýhappens when G is reductive. However, Nagata discovered aÌýcounterexample for a choice of non-reductive G, which Mukai laterÌý generalised. We will go over this construction of Mukai’s. If timeÌýpermits, we will mention a more recent result of Bérczi, Doran andÌýKirwan regarding the finite generation of the subring of invariantsÌýwhen G is not assumed to be reductive.