Preface. 1 Signals and Signal Spaces: A Structural Viewpoint. 1.1 What is a Signal? 1.2 Spaces and Structures. 1.3 Signal Spaces and Systems. 1.4 Linearity, Shift-Invariance and Causality. 1.5 Convolutional Algebra and the Z-Transform. 1.6 Shifts, Transforms and Spectra. 2 Algebraic Preliminaries. 2.1 What's in a Definition? 2.2 Set Theoretic Notation. 2.3 Relations and Operations. 2.4 Groups. 2.5 Vector Spaces. 2.6 Posets, Lattices, and Boolean Algebras...