This chapter formalizes the Ideal Flow Network (IFN) framework, moving from conceptual intuition to a rigorous mathematical foundation. The chapter then establishes the foundational axioms that govern flow behavior within the IFN paradigm, including the principle of conservation of flow and the non-negativity of the flow matrix. The core of the chapter is the derivation of the Ideal Flow matrix, which is shown to be the unique steady-state solution of a Markov chain, with its existence and properties guaranteed by the Perron-Frobenius theorem. This mathematical formalism provides a clear, logical basis for understanding how network structure inherently shapes traffic patterns. By the end of the chapter, readers will possess a solid theoretical understanding of the core machinery of Ideal Traffic Assignment, preparing them for the advanced analyses in subsequent chapters.