Finding outlier regions within a time series is essential in many application domains reaching from self-driving cars, finance, and marketing to medical diagnosis and cyber-physical systems in the industry. To that end, this thesis develops a new method to detect outlier regions within time series based on self-supervised deep learning that recently has played a crucial role in facilitating deep anomaly detection on images, where powerful dataaugmenting geometric transformations are available. However, such transformations are widely unavailable for time series data. Addressing this, the proposed method, Local Neural Transformations (LNT), learns local time series transformations from data. Furthermore, the method produces an anomaly score for each time step and thus can be used to detect outliers on a sub-sequence level. Extensive experiments demonstrate that LNT can find synthetic noise in speech segments from the LibriSpeech data set and better detect interruptions to cyber-physical systems than previous work. The choice of components is justified in theoretical analysis and ablation studies, and visualizations of the learned transformations give insights into the type of transformations that LNT learns. In summary, this thesis demonstrates that the paradigm of self-supervised learning can also be successfully extended for outlier region detection in time series and thus gives new directions for future research.