This book contains the latest developments in a central theme of research on analysis of one complex variable. The material is based on lectures at the University of Michigan. The exposition is about understanding the geometry of interpolating and sampling sequences in classical spaces of analytic functions. The subject can be viewed as arising from three classical topics: NevanlinnaPick interpolation, Carleson's interpolation theorem for \(H^\infty\), and the sampling theorem, also known as the WhittakerKotelnikovShannon theorem. The author clarifies how certain basic properties of the space at hand are reflected in the geometry of interpolating and sampling sequences. Key words for the geometric descriptions are Carleson measures, Beurling densities, the Nyquist rate, and the HelsonSzegő condition. Seip writes in a relaxed and fairly informal style, successfully blending informal explanations with technical details. The result is a very readable account of this complex topic. Prerequisites are a basic knowledge of complex and functional analysis. Beyond that, readers should have some familiarity with the basics of \(H^p\) theory and BMO. Readership Graduate students and research mathematicians interested in analysis. Table of Contents  Carleson's interpolation theorem
 Interpolating sequences and the Pick property
 Interpolation and sampling in Bergman spaces
 Interpolation in the Bloch space
 Interpolation, sampling, and Toeplitz operators
 Interpolation and sampling in PaleyWiener spaces
 Bibliography
 Index
