- "Number Fields and Function Fields: Two Parallel Worlds" (2007): This book provides an introduction to algebraic number theory and function fields, drawing connections between these two areas of mathematics.
- "Algebraic Number Theory" (2010, with Alfred Weiss): This textbook covers various topics in algebraic number theory, including algebraic integers, p-adic numbers, and class field theory.
- "Elliptic Curves and Modular Forms" (2012, with Christophe Diem): This book offers an introduction to elliptic curves and modular forms, with a focus on their arithmetic and geometric properties.
- "Computing Class Groups: An Overview" (2015, with Florian Heß and Christophe Ritzenthaler): This article surveys algorithms for computing class groups, which play a fundamental role in algebraic number theory.
- "Quantum Algorithms and Computational Number Theory" (2016, with Helger Lipmaa and Michele Mosca): This article discusses the potential impact of quantum computing on number theory and cryptographic applications.
- "Solving Polynomial Equations" (2020, with Alexander Fuchs): This book presents algebraic and numerical techniques for solving polynomial equations, emphasizing algorithmic aspects.
In addition to these publications, Tilmann Kleinjung has also written numerous research articles and conference proceedings on topics such as computational algebra, cryptography, and arithmetic geometry. His research has garnered recognition in the mathematical community, and he has received awards for his contributions.