chapter On free complete intersections -- chapter On the number of ideals of finite colength -- chapter Realizable Sequences Linked to the Hilbert Function of a 0-Dimensional Projective Scheme -- chapter Lexsegment ideals in the exterior algebra -- chapter On the equations defining toric projective varieties -- chapter KRS and determinantal ideals -- chapter The Koszul complex in projective dimension one -- chapter Grobner bases as Characteristic Sets -- chapter 3 folds with degenerate secant variety: on a theorem of G. Scorza.