Introduction.- Part 1 Foil Theories.- Optimal Information Transfer and Real-Vector-Space Quantum Theory (William K. Wootters).- Almost quantum theory (Benjamin Schumacher, Michael D. Westmoreland).- Quasi-quantization: classical statistical theories with an epistemic restriction (Robert W. Spekkens).-Part 2 Axiomatizations.- Information-theoretic postulates for quantum theory (Markus P. Müller, Lluís Masanes).- Quantum from principles (Giulio Chiribella, Giacomo Mauro D'Ariano, Paolo Perinotti).- Reconstructing Quantum Theory (Lucien Hardy).- The classical limit of a physical theory and the dimensionality of space (Borivoje Dakic, Časlav Brukner).- Some Negative Remarks on Operational Approaches to Quantum Theory (Christopher A. Fuchs, Blake C. Stacey).- Generalised Compositional Theories and Diagrammatic Reasoning (Bob Coecke, Ross Duncan, Aleks Kissinger, Quanlong Wang).Part 3 Categories and ordered vectors spaces.- Post-Classical Probability Theory (Howard Barnum and Alexander Wilce).- Information causality (Marcin Pawlowski, Valerio Scarani).- Part 4 Quantum correlations.- Macroscopic locality (Miguel Navascués).- Guess your neighbour's input: no quantum advantage but an advantage for quantum theory (Antonio Acın, Mafalda L. Almeida, Remigiusz Augusiak, Nicolas Brunner).- The completeness of quantum theory for predicting measurement outcomes (Roger Colbeck, Renato Renner).