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We study the moduli space F_{2d} of polarised K3 surfaces of degree 2d. Wecompute all relations between Noether-Lefschetz divisors on these moduli spacesfor d up to around 50. This leads to a very concrete description of therational Picard group of F_{2d}. We show how to determine the coefficients ofboundary components of relations in the rational Picard group, giving relationson a (toroidal) compactification of F_{2d}. We draw conclusions from this aboutthe Kodaira dimension of F_{2d}, in many cases confirming earlier results byGritsenko, Hulek and Sankaran, and in two cases giving a new result.  This is an abridged version of the PhD thesis by the same author.

Modular forms on the moduli space of polarised K3 surfaces