  As machine learning technology gets applied to actual products and solutions,
new challenges have emerged. Models unexpectedly fail to generalize to small
changes in the distribution, tend to be confident on novel data they have never
seen, or cannot communicate the rationale behind their decisions effectively
with the end users. Collectively, we face a trustworthiness issue with the
current machine learning technology. This textbook on Trustworthy Machine
Learning (TML) covers a theoretical and technical background of four key topics
in TML: Out-of-Distribution Generalization, Explainability, Uncertainty
Quantification, and Evaluation of Trustworthiness. We discuss important
classical and contemporary research papers of the aforementioned fields and
uncover and connect their underlying intuitions. The book evolved from the
homonymous course at the University of T\"ubingen, first offered in the Winter
Semester of 2022/23. It is meant to be a stand-alone product accompanied by
code snippets and various pointers to further sources on topics of TML. The
dedicated website of the book is https://trustworthyml.io/.
