This book covers topics appropriate for a first-year graduate course preparing students for the doctorate degree. The first half of the book presents the core of measure theory, including an introduction to the Fourier transform. The second half of the book treats basic functional analysis. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and c*-algebras. lt concludes with a characterization of the unitary equivalence classes of normal operators on a Hilbert space. The book is self-contained and only relies on a background in functions of a single valuable and the elements of metric spaces. Following the author’s belief that the best way to learn is to start with the particular and proceed to the more general, it contains numerous examples and exercises.