This book is meant as a text for a first-year graduate course in analysis. In a sense, the subject matter covers the same topics as elementary calculus - linear algebra, differentiation, integration - but treated in a manner suitable for people who will be using it in further mathematical investigations. The book begins with point-set topology, essential for all analysis. The second part deals with the two basic spaces of analysis, Banach and Hilbert spaces. The book then turns to the subject of integration and measure. After a general introduction, it covers duality and representation theorems, some applications (such as Dirac sequences and Fourier transforms), integration and measures on locally compact spaces, the Riemann-Stjeltes integral, distributions, and integration on locally compact groups. Part four deals with differential calculus (with values in a Banach space). The next part deals with functional analysis. §It includes several major spectral theorems of analysis, showing