Hilbert Modular Forms

This book provides a comprehensive overview of the Hilbert modular group and Hilbert modular forms, focusing on singular cohomology and its Hodge decomposition. It consolidates important results previously found in scattered research papers, offering elementary and complete proofs. Key topics include reduction theory, the trace formula, Shimizu's formulae, and the work of Matsushima and Shimura. Appendices cover essential concepts such as algebraic numbers and Hodge theory, making it accessible to students familiar with complex analysis and algebra.