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Focusing on l-adic cohomology, this book presents an accessible introduction to etale and l-adic cohomology theory, including monodromy theory related to Lefschetz pencils. Originally prepared as notes for a conference on Deligne's proof of the Weil conjectures, the authors expanded these notes to provide a self-contained exploration of the topic. It incorporates historical insights from Professor J. A. Dieudonne and has been translated into English, thanks to the efforts of Professor W. Waterhouse and his wife.

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.

All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included