The thermodynamics of interacting homonuclear dimers adsorbed on homogeneous surfaces in-a monolayer regime is addressed. Dimer adsorption is described in the framework of the lattice gas theory. Hypercubic lattices are used as a model of homogeneous substrate in one and two dimensions. The effect of lateral interactions on the behavior of the adlayer is considered. The adsorption isotherm, energy of adsorption, differential heat of adsorption, and configurational entropy are obtained by Monte Carlo simulations and compared with analytical calculations. Particular attention is devoted to the two-dimensional case with repulsive nearest neighbor lateral interactions in the critical and subcritical regime. Different ordered phases are observed and their relationship with the behavior of the thermodynamic functions of the adsorbed monolayer is shown.