Texts written in simplified language are essential for accessible communication. However, manually writing accessible texts or simplifying difficult-to-read texts into accessible language is very time-consuming. Machine learning models such as large language models (LLMs) can assist with this intra-lingual translation task by providing drafts for professional translators. This volume takes a computational linguist's perspective on automatic text simplification (ATS), providing a broad introduction to the field. The book begins by introducing the challenges and opportunities. It also explains how to build simplification datasets, use them to train machine learning models, and evaluate them. The book also provides state-of-the-art overviews of German text simplification models, datasets and evaluation metrics for document and sentence simplification. While the focus is primarily on German plain language ("Einfache Sprache"), the book also provides some insights into German easy-to-read language ("Leichte Sprache") and other languages.