This report presents the basic design of a rocket engine injector and combustion chamber for saturated nitrous oxide and liquid ethanol, as well as details of the construction and operation of the engine in which the injectors will be used. At first, an oxidant-fuel mixture is selected based on a thermochemical analysis that explores several existing options and other combinations that have not yet been studied. As a result, nitrous oxide is chosen as an oxidant and ethanol as fuel. Then a simplified methodology is proposed for the design of a pressure-swirl injector responsible for ethanol. Computational fluid dynamics is used to verify the validity of the above-mentioned analysis, using Volume of Fluid (VOF). For the nitrous oxide injector, the flash-boiling phenomenon is investigated, verifying its importance for the ongoing project. The effect is treated analytically using the Dyer model to account for non-equilibrium thermodynamics. Simplified zero-dimensional and one-dimensional combustion models are explored as tools to design the rocket combustion chamber. Furthermore, combustion instability due to acoustic phenomena is studied, with the first spinning tangential mode being computed for the herein developed motor and an ensemble of acoustic cavities being developed to suppress the aforementioned mode. Finally, a preliminary diagram of the static test bench which will be used to validate the injectors and the designed engine is also presented.