The power production of downstream wind turbines in a wind farm is significantly impacted by wake effects of upstream turbines. Improving the layout optimization process could reduce these wake losses and therefore result in more efficient wind farms. The wakes are also affected by atmospheric stability conditions, as stable conditions lead to a reduced wake recovery, and unstable conditions lead to an improved wake recovery. The topic of atmospheric stability has quickly gained more attention in wind energy research over the recent years. However, there is still little research done that focuses specifically on the effects of atmospheric stability on the wind farm layout optimization process. This thesis aims to determine the effects of atmospheric stability on the optimal layout of a wind farm and to quantify the potential benefits of considering stability conditions in the layout optimization process. A stability-dependent Jensen wake model is developed, using a stability-dependent wake decay coefficient based on the non-dimensional Obukhov length. The developed model is implemented in FLORIS, a wake modeling utility for Python, to calculate the wind field and the annual energy production (AEP). A simplistic layout optimization method is used, in which the positioning of wind turbines relative to each other is fixed and only the orientation of the entire wind farm is varied. To quantify the potential benefits of considering stability conditions, the layout optimization is done twice for each analyzed case: once using the determined stability conditions and once using the assumption of neutral stability conditions. The resulting benefit of considering stability effects is expressed as the potential AEP gain. The results of the first cases looked promising, showing potential AEP gains of 7.4%, 5.6%, and 9.2%. However, these cases consist of unrealistic wind conditions and were mostly intended to study the effects of different stability conditions on the resulting optimal layout. For example, it is found that it is more beneficial to reduce wake overlap for stable conditions than for unstable conditions, which results in stable wind directions playing a dominant role in the optimization process. Cases with semi-realistic wind conditions showed significantly lower potential AEP gains of 0.1% and 0.7%. Finally, a real case based on meteorological data from an offshore site in the Netherlands resulted in a potential AEP gain of 0.0%. It is concluded that the benefits of considering stability effects in the layout optimization process are likely to be insignificant. In most cases, the layout optimization under neutral stability conditions already optimizes for wind directions with stable conditions, as stable conditions tend to be more frequent in wind directions with high wind speeds. It is expected that there can be a small potential AEP gain in cases with unusual stability distributions that differ significantly from the described trend. However, even in such cases it is likely that the benefits are still very small.