Just as a multinomial sample can be classified by the levels of two factors, a multinomial sample can also be classified by the levels of three factors. Section 3.1 begins with a discussion of Simpson’s paradox and the need for tables with more than two factors. Section 3.2 discusses independence and odds ratio models for three-dimensional tables under multinomial sampling. Section 3.3 examines the iterative proportional fitting algorithm for finding estimates of expected cell counts. Section 3.4 introduces log-linear models for three-dimensional tables. Section 3.5 considers the modifications necessary for dealing with product-multinomial sampling and comments on other sampling schemes. Section 3.6 introduces model selection criteria and Sect. 3.7 introduces tables with four of more dimensions.