In this paper we provide the mathematical presentation of the RHOMOLO model. In addition, we perform some stylized and illustrative simulations with the aim to make the reader familiar with the economic adjustment mechanisms incorporated into the model. Essentially, we attempt to offer the reader and the potential users of the model an intuition of the transmission channels existing in the current version RHOMOLO. The analysis is kept simple to facilitate a better understanding of the model's findings. We simulate a permanent demand-side shock implemented separately for each of the 267 regions contained in the model. We repeat the same simulation under three alternative labour market closures and three different imperfectly competitive product market structures.