This paper presents a new formulation of statistical thermodynamics for classical fluids where molecules can associate into dimers and higher-order aggregates due to highly directional attractive forces. The approach involves decomposing the pair potential into repulsive and directionally attractive components and using this in the expansion of the logarithm of the grand partition function in fugacity graphs. The directional attraction is used to classify graphs and introduce a topological reduction, replacing fugacity with two variables: singlet density ρ and monomer density ρ₀. Thermodynamic functions are expressed as graph sums, and pair correlations are analyzed using a matrix analog of the direct correlation function. The low-density limit is treated exactly, while the Mayer expansion, which uses only ρ, leads to significant difficulties. The paper illustrates the complexity of resumming the Mayer expansion for dimers. The paper discusses the challenges of modeling fluids with highly directional forces, emphasizing the need to incorporate interaction geometry early. It contrasts the conventional singlet density expansion with the fugacity expansion, which is simpler and more effective. The two-density theory, based on ρ and ρ₀, is shown to be superior, as it trivially captures the low-density limit of a dimerizing gas, while the Mayer ρ-expansion requires complex graph resummation. The paper also introduces a model potential that combines repulsive and directional attractive components, allowing for a wide range of physical scenarios. The approach differs from physical cluster theories, leading naturally to a two-density formulation of statistical thermodynamics. The paper highlights the importance of considering the geometry of interactions and the advantages of using the fugacity expansion over the singlet density expansion.This paper presents a new formulation of statistical thermodynamics for classical fluids where molecules can associate into dimers and higher-order aggregates due to highly directional attractive forces. The approach involves decomposing the pair potential into repulsive and directionally attractive components and using this in the expansion of the logarithm of the grand partition function in fugacity graphs. The directional attraction is used to classify graphs and introduce a topological reduction, replacing fugacity with two variables: singlet density ρ and monomer density ρ₀. Thermodynamic functions are expressed as graph sums, and pair correlations are analyzed using a matrix analog of the direct correlation function. The low-density limit is treated exactly, while the Mayer expansion, which uses only ρ, leads to significant difficulties. The paper illustrates the complexity of resumming the Mayer expansion for dimers. The paper discusses the challenges of modeling fluids with highly directional forces, emphasizing the need to incorporate interaction geometry early. It contrasts the conventional singlet density expansion with the fugacity expansion, which is simpler and more effective. The two-density theory, based on ρ and ρ₀, is shown to be superior, as it trivially captures the low-density limit of a dimerizing gas, while the Mayer ρ-expansion requires complex graph resummation. The paper also introduces a model potential that combines repulsive and directional attractive components, allowing for a wide range of physical scenarios. The approach differs from physical cluster theories, leading naturally to a two-density formulation of statistical thermodynamics. The paper highlights the importance of considering the geometry of interactions and the advantages of using the fugacity expansion over the singlet density expansion.