Economists describe the stock market as an efficient market so that there is no way to forecast its future prices. Rapid development in computational power has led to machine learning techniques with stronger predictive power becoming more prominent. \\
The scope of this thesis is to examine artificial neural networks' ability to forecast the Danish stock market. A total of six Danish stocks are forecasted using daily one-step-ahead forecasting. The time period used for this purpose is the year between 2010 and 2019, where the first eight years is used for training and testing, while the last is used for forecasting. \\
Different architectures are tested, including FNN, RNN, LSTM, GRU, bi-LSTM, and bi-GRU. Each architecture is tested both with and without the inclusion of extra explanatory variables. In order to evaluate the models' forecasts, ARIMA and ARIMAX are used as baseline models.\\
The simpler FNN structure without the addition of explanatory variables proved, via out-of-sample forecasting, to be the more accurate of the artificial neural network models. The forecasts from the FNN models were, in four of the six stocks forecasted, statistically less accurate when compared to the forecasts from the ARIMA and ARIMAX models. It was found that ANNs need further development before their usage in forecasting stock market prices becomes feasible.