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The 21 assumptions which underlie the Geometry published in Hilbert's 
classic text Grundlagen der Geometrie. The eight Incidence Axioms concern collinearity and intersection and include the first
of Euclid's Postulates. The four Ordering Axioms concern the arrangement of points, the five
Congruence Axioms concern geometric equivalence, and the three Continuity Axioms concern continuity. There
is also a single parallel axiom equivalent to Euclid's Parallel Postulate.
See also Congruence Axioms, Continuity Axioms, Incidence Axioms, Ordering Axioms, Parallel Postulate
References
Hilbert, D. The Foundations of Geometry, 2nd ed. Chicago, IL: Open Court, 1980.
Iyanaga, S. and Kawada, Y. (Eds.). ``Hilbert's System of Axioms.'' §163B in
Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 544-545, 1980.