Abstarct: ‎ ‎Data from many phenomena in various disciplines such as health‎, ‎environment‎, ‎urban management‎, ‎and sports are usually spatial or spatio-temporal dependent counts‎. ‎The traditional model for analyzing count data is the Poisson model‎. ‎However‎, ‎this model is not suitable in most situations due to having equal mean and variance‎. ‎Most of the count data we deal with is usually over-or under-dispersed‎. ‎Multiple models have been developed to consider such inherent features of count data‎. ‎This dissertation creates a spatial and spatio-temporal gamma count model that is flexible enough in the dispersion modeling of count responses‎. ‎We use an approximate Bayesian approach baxsed on the integrated nested Laplace approximation (INLA) for fitting and inference in the proposed model‎. ‎We examine various applications of the model and evaluate its performance compared to competing models using both simulation and real-world examples‎.