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 subject 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 special theory. the text assumes a background in measure theory and Lebesgue integration and offers historical references and numeric exercises.