"Idempotent Analysis and Its Applications" is a specialized book that deals with the theory of idempotent algebra and its diverse applications across various disciplines. The book begins with an introduction to idempotent analysis, covering fundamental concepts such as idempotent semirings and idempotent linear algebra. These areas are crucial for understanding systems of equations that are linear in an idempotent semiring. The work also highlights historical developments, such as the early investigations by S. Kleene, and demonstrates the relevance of idempotent algebra in theoretical computer science, biomathematics, logic, mathematical physics, mathematical economics, and optimization. With a comprehensive overview of the literature and key facts about idempotent algebra, this book serves as a valuable resource for students and professionals interested in these topics.