Andreas Demleitner is a mathematician whose research focuses on complex algebraic geometry, with a particular emphasis on the geometry of torus quotients and their moduli. He completed his Ph.D. at the University of Bayreuth in 2020 under the supervision of Prof. Dr. Fabrizio Catanese, working on the structure and classification of complex varieties. Afterwards, he held a postdoctoral position at the University of Freiburg with Prof. Dr. Stefan Kebekus, further developing his research on quotients of complex tori. His work contributes to a deeper understanding of the relationships between complex structures, group actions, and moduli spaces in algebraic geometry. In addition to research, Dr. Demleitner greatly enjoys teaching and sharing mathematical ideas. He has actively participated in academic collaborations and international conferences, engaging with the broader mathematical community and fostering the exchange of ideas across diverse areas of geometry.

• Chapter 1. Introduction.- Chapter 2. A Short Group-Theoretic Account.- Chapter 3. Prerequisites on Complex Tori and Hyperelliptic Manifolds.- Chapter 4. Group-Theoretical Properties of Hyperelliptic Groups.- Chapter 5. Outline of the Classification.- Chapter 6. Abelian Hyperelliptic Groups.- Chapter 7. The 2-Sylow Subgroups of Hyperelliptic Groups in Dimension 4.- Chapter 8. The 3-Sylow Subgroups of Hyperelliptic Groups in Dimension 4.- Chapter 9. An Alternative Way of Determining the 2- and 3-Sylow Subgroups.- Chapter 10. Hyperelliptic Groups in Dimension 4 whose Order is 2ᵃ·3ᵇ.- Chapter 11. Hyperelliptic Groups in Dimension 4 whose Order is Divisible by 5 or 7.- Chapter 12. The Canonical Divisor of a Hyperelliptic Manifold.- Chapter 13. Final Remarks and Further Questions.