Accurate forecasts are essential for integrating wind energy into the power grid. With wind energy's growing role in the renewable mix, precise short-term generation forecasts are increasingly vital. Turbine-level forecasts are critical for optimal wind farm operation, control, and planning. However, the wind's unpredictability and the complex interactions between turbines make forecasting challenging. Existing methods either depend on resource-intensive physical models or overlook turbine interactions, resulting in isolated, overly simplistic models. This master's thesis explores the use of Graph Neural Networks (GNNs) in conjunction with Recurrent Neural Networks (RNNs) for wind power generation forecasting in wind farms. The result is an integrated approach that can learn the interactions between turbines through GNNs to handle the temporal dynamics of the data through RNNs. The research begins with an in-depth overview of wind turbines and their arrangement in wind farms, highlighting the importance and challenges of Wind Power Forecasting (WPF). It establishes that the spatial configuration of turbines complicates power generation estimation, especially over different time horizons. Graphs are introduced as an effective way to represent the interconnections between turbines. Various methods for constructing these graphs are reviewed, focusing on predefined heuristics and their limitations in adapting to changing wind farm characteristics. The core of this thesis is the AG-LSTM Network, a model that integrates RNNs and GNNs for short-term WPF for turbines within a wind farm. It utilizes historical power generation data, a variety of future and past covariates, and static turbine-specific features. The model is based on an encoder-decoder architecture with an Adaptive Graph Long-Short Term Memory Cell (AG-LSTM), which generates a dynamic adjacency matrix representing the farm's state at each moment. This matrix combines the input features and hidden states across turbines, resulting in an embedding that is transformed into the power forecast. Through comprehensive experiments and analyses, the AG-LSTM Network proves to be more accurate than state-of-the-art methods on two real-life datasets when future covariates are unavailable. Further experiments demonstrate the quality of the forecast and break down the contribution of the different choices regarding its architecture. The results underscore the potential of hybrid neural network architectures in enhancing WPF, providing a valuable tool for the renewable energy sector. In conclusion, this research contributes to the renewable energy field by proposing a novel hybrid neural network model that effectively addresses the complexities of short-term WPF. Future work could explore further exploitation of future covariates and the robustness of the model against incomplete input data.