Section I: Introduction to Mental representations of magnitudes Mental Magnitudes Objects, sets and ensembles Attentional mechanisms for counting in stabilized and in dynamic displays Section II: Introduction to Neural codes for space, time and number Plurality of the brain's spatial representation system Temporal Neuronal Oscillations can Produce Spatial Phase Codes Population Clocks: Motor Timing with Neural Dynamics Discrete neuroanatomical substrates for feedforward versus feedback mechanisms of temporal prediction The neural code for number Section III: Introduction to hared mechanisms, links and metaphors Synaesthesia: A positive cognitive neuroscience approach to studying time, number and space How is number associated with space? The role of working memory Biases in spatial and numerical bisection: a causal link? Compression of the perceptual metric during saccadic eye movements Section IV: Introduction Ontogeny and phylogeny Origins of spatial, temporal and numerical cognition: Insights from animal model systems The approximate number system and the computations it supports as evidenced from a non-human primate model Origins of generalized magnitude representation Section V: Introduction to Development, education and representational change Foundational numerical capacities and the origins of dyscalculia Neurocognitive start-up tools for symbolic number representations Sources of Abstract Concepts: Natural Number and Natural Geometry Geometry as a universal mental construction How languages construct time Improving low-income children's number sense.

1. Mental magnitudes and their transformations -- 2. Neural codes for space, time and number -- 3. Shared mechanisms for space, time and number -- 4. Origins of proto-mathematical intuitions -- 5. Representational change and education.