About This Book: This book introduces functional analysis, a branch of mathematics that examines topological algebraic structures and their application in solving analytical problems. It provides a foundational understanding of topological vector spaces, emphasizing both theory and practical applications. While the subjects is vast,the book makes selective choices to maintain a manageable size. It covers various topics without requiring local convexity assumptions and explores applications in areas like distribution theory, fourier transforms, and spectral theory. The text assumes a background in measure theory and lebesgue integration and offers historical references and numerous exercises. Overall, it delivers a balanced introduction to functional analysis, focusing on core concepts and their real world relevance.