This analysis book for mathematics students starting from the third semester continues the volumes "A Bit of Analysis" and "A Bit More Analysis." The starting point of this volume is a clear and powerful presentation of Lebesgue theory, which does not rely on the rather complex measure theory as a foundation. It includes the transformation formula with a new proof, integration on manifolds with Stokes' theorem, and the classical theorems of vector analysis. Following this, the essential foundations of L^p spaces, the Hilbert space theory of Fourier series, Fourier transformation, and distributions are covered. The book concludes with an introduction to function theory, which is the theory of differentiable functions in a complex variable. Each chapter includes numerous exercises, with complete solutions available on the publisher's website.