Independent assortment answers the question of what happens when two parent cells differ in two or more genes. Mendel discovered independent assortment when he performed experiments called dihybrid crosses. Dihybrid crosses are crosses between two individuals that are heterozygous at two genes, for example AaBb & AaBb.
Let's look at how a dihybrid cross works in order to see how independent assortment works. Consider that the inflated pea pod shape (I) is dominant over the deflated pea pod shape (i). Also consider that the pea pod color green (G) is dominant over the pea pod color yellow (g).
If there is no such thing as independent assortment the following thing will occur in the picture below.
Without independent assortment the expected outcome will be a three to one ratio. This can be shown through a Punnett square.
If there is such a thing as independent assortment in which the traits on different chromosomes separate independently from each other the expected ratio will be 9:3:3:1. This also can be shown through a Punnett square.
Mendel found that independent assortment is what really happens. He therefore came up with the law of independent assortment which states that alleles of different genes assort independently from one another during gamete formation. What is important here is to remember that independent assortment happens when genes are on different chromosomes. Independent assortment does not hold true for genes that are on that same chromosome because if two genes are close enough together on the same chromosome then they may be linked in which case they stay together while crossing over. This phenomenon is called linkage.
Independent assortment tutorial illustrates the law of independent assortment and discusses the exceptions to this law.
Beyond Mendel goes a little bit father than what Mendel discovered. This page also includes practice problems dealing with genetics.