This chapter introduces the concept of error function in order to quantitatively investigate errors. First of all, error function is categorized according to the differences in the range of error values and the objects of interest. Scalar and vector functions are then examined. The process of building error function is discussed based on different rules in judging errors. Last but not the least, the relationship between values of error functions under different rules of judging errors and three propositions are obtained accordingly. This chapter mainly seeks to quantify the errors in the models of error system, which makes it possible for the models of error systems to be widely applied in practice.