This book investigates the theory of automorphic forms of several variables, a complex area of number theory and algebraic geometry. The author, I. Satake, a distinguished mathematician, presents a rigorous treatment of the subject, drawing upon advanced concepts from Lie groups, harmonic analysis, and algebraic geometry. The work is intended for researchers and graduate students in mathematics, providing a comprehensive overview of the fundamental principles and key results in the field.

This monograph is recognized as a significant contribution to the study of automorphic forms, offering a deep and comprehensive treatment of the subject. Its rigorous approach and advanced mathematical content position it as a key reference for specialists in number theory and related fields. The work is valued for its thoroughness and the author's expertise in synthesizing complex theoretical frameworks.