What is the Hardy-Weinberg principle and under what conditions does this principle apply?

It is often stated as either a law or principle or just H-W equations for a population at equilibrium

The H-W equation is the mathematically stated relation ship between a populations genotypes and its allele frequencies.       p+q = 1 & q^2 + 2pq + q^2 = 1
 f(p) = the frequency of the dominant allele in the population & f(pp) = frequency of the dominant genotype in the population  etc.
http://www.iscid.org/encyclopedia/Hardy-Weinberg_Law"The Hardy-Weinberg principle states that in a large randomly breeding population, allelic frequencies will remain the same from generation to generation assuming that there is no mutation, gene migration, selection or genetic drift."  Clearly this is a case of perfect equilibrium in a static population under no selection pressures and with the unnatural condition of perfect replication so no mutations are introduced. It is further simplified by considering only two of the many alleles likely to be present in a population for any given gene.