Projective geometry is developed axiomatically. Axioms for affine and projective planes are given. Duality is investigated and Desargues’ Theorem proved for projective planes that arise as planes in a projective 3-space. Pappus’ Theorem and projective planes over division rings are introduced. The last section is dedicated to proving that every projective plane where Desargues’ Theorem holds is a projective plane over a uniquely determined division ring and that this division ring is commutative if Pappus’ Theorem holds as well.