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Sign language is an important factor in the integration of deaf and hard of hearing people into society. Due to the limited number of people who speak sign language, there is a communication barrier that needs to be addressed. In recent years, sign language has been an important field of research. There have been numerous attempts at trying to find a solution to this problem. This thesis focuses on the German finger alphabet, which has not been researched as much. It examines whether it is possible to recognize the gestures of the German finger alphabet in real time with a convolutional neural network. For that, literature is consulted, and a prototype is developed. The prototype includes a newly created dataset with 2,500 images distributed over 25 gestures, a convolutional neural network, and software for real-time translation of a video stream. The prototype demonstrates the feasibility of realizing such a task. The convolutional neural network achieves an accuracy of 99.61%. On a powerful desktop computer, the prediction of a single frame takes between 36 and 40 ms. However, there are some limitations and restrictions to the quality of prediction caused by factors such as lighting and background. Additionally, certain similar gestures, such as M and N, are difficult to distinguish. Based on these results, ideas and suggestions for future studies are presented.