The purpose of this book is to provide a perspective and foundation for DIF, a review DIF approaches. Further, DIF methohds classified into two categories: IRT methods and non-IRT methods, respectively. For the former, the estimation of an IRT model is required, and a statistical testing procedure is followed, based on the asymptotic properties of statistics derived from the estimation results. For the latter, the detection of DIF items is usually based on statistical methods for categorical data, with the total test score as a matching criterion. Item Response Theory (IRT) techniques provide a powerful means of testing items for bias, using what is known as differential item functioning (DIF) analysis. In contrast, Classical Test Theory (CTT) based methods of assessing bias are fundamentally limited, especially approaches that base their assessment of bias on the presence of group mean differences in total tests scores across demographic groups. This book provides different studies to detect a gender related DIF in mathematics