A projective plane of order q is an incidence structure of points and lines with q+1 points on each line and q+1 lines through each point, where two points determine a unique line and two lines intersect in a unique point. It is easy to see that there must be precisely q^2+q+1 points and the same number of lines. q>1 is assumed. There are very many constructions of plane of prime-power orders, but none of non-prime-power orders. The "classical" projective plane is one defined over a field. For the finite field GF(q), where q is a power of a prime, the resulting plane is the Desarguesian plane PG(2,q). But There are constructions of other planes of order q a prime power. This question is probably the number one question in finite geometry. The smallest case where a plane is not known and not proved to be impossible is order 12.