Sampling Theory a Renaissance : Compressive Sensing and Other Developments Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics science and engineering. A multitude of tools designed to recover hidden information are based on Shannon’s classical sampling theorem a central pillar of Sampling Theory. The growing need to efficiently obtain precise and tailored digital representations of complex objects and phenomena requires the maturation of available tools in Sampling Theory as well as the development of complementary novel mathematical theories. Today research themes such as Compressed Sensing and Frame Theory re energize the broad area of Sampling Theory. This volume illustrates the renaissance that the area of Sampling Theory is currently experiencing. It touches upon trendsetting areas such as Compressed Sensing Finite Frames Parametric Partial Differential Equations Quantization Finite Rate of Innovation System Theory as well as sampling in Geometry and Algebraic Topology Part I: Sparsity Models Estimation in High Dimensions: A Geometric Perspective Convex Recovery of a Structured Signal from Independent Random Linear Measurements Low Complexity Regularization of Linear Inverse Problems Part II: Frames with Benefits Noise shaping Quantization Methods for Frame based and Compressive Sampling Systems Fourier Operations in Applied Harmonic Analysis. The Fundamentals of Spectral Tetris Frame Constructions Part III: Bandlimitation Recast System Approximation and Generalized Measurements in Modern Sampling Theory Entire Functions in Generalized Bernstein Spaces and Their Growth Behavior Sampling and Geometry A Sheaf theoretic Perspective on Sampling Part IV: Solutions of Parametric PDEs How to Best Sample a Solution Manifold On the Stability of Polynomial Interpolation using Hierarchical Sampling Part V: Implementation OperA: Operator based Annihilation for Finite Rate of Innovation Signal Sampling Digital Adaptive Calibration of Data Converters using Independent Component Analysis