Synopsis These notes are a record of a one semester course on Functional Analysis given by the author to second year Master of Statistics students at the Indian Statistical Institute, New Delhi. Students taking this course have a strong background in real analysis, linear algebra, measure theory and probability, and the course proceeds rapidly from the definition of a normed linear space to the spectral theorem for bounded selfadjoint operators in a Hilbert space. The book is organised as twenty six lectures, each corresponding to a ninety minute class session. This may be helpful to teachers planning a course on this topic. Well prepared students can read it on their own.