The Analytical Network Process (ANP) is a multicriteria decision analysis method that has been widely used the last few years to support decision making. Primary aim of this paper is to expose in detail the mathematics of the method in order to explain the mechanics of its steps and provide an exact algorithm that will give the opportunity to easily understand and implement either the method itself or modified versions of it. The paper holds an holistic approach to the method, covering not only simple ANP models but also Hierarchies and BOCR models. The practical implication of this paper is that the algorithm provided may be used as a basis for the development of custom software programs and tools that will foster the further expanding of the method.