According to the Mendel's law the phenotypical characteristics would be determined by pair of factors (alleles) that separate independently in gametes. What are the major types of inheritances that are exceptions to Mendel's rules?

There are many kinds of inheritance that don't follow the mendelian pattern. Remarkable among them are: gene interactions (complementary genes, epistasis and quantitative, or polygenic, inheritance), multiple alleles, linkage without or with crossing over and sex-linked inheritance.

The Pleiotropy lacking of dominance and lethal genes do not fit as variations of inheritance ever since genes can have these behaviors and at the same time obey mendelian laws.

The Mutations and the Aneuploidies are abnormalities that also alter the mendelian pattern of inheritance as well as mitochondrial inheritance (passage of mitochondrial DNA from the mother through the cytoplasm of the egg cell to the offspring).