Permutation Testing for Isotonic Inference on Association Studies in Genetics The purpose of this book is to illustrate a new statistical approach to test allelic association and genotype specific effects in the genetic study of diseases. There are some parametric and non parametric methods available for this purpose. We deal with population based association studies but comparisons with other methods will also be drawn analysing the advantages and disadvantages of each one particularly with regard to power properties with small sample sizes. In this framework we will work out some nonparametric statistical permutation tests and likelihood based tests to perform case control analyses to study allelic association between marker disease gene and environmental factors. Permutation tests in particular will be extended to multivariate and more complex studies where we deal with several genes and several alleles together. Furthermore we show simulations under different assumptions on the genetic model and analyse real data sets by simply studying one locus with the permutation test. Introduction Association Studies in Genetics The Nonparametric Permutation Methodology Statistical Problems of Allelic Association Power and Sample Size Simulations Case Study Conclusions References.