Intro; Foreword; Preface; Contents; 1 Neutron Stars Formation and Core Collapse Supernovae; 1.1 Introduction; 1.1.1 Core-Collapse Supernovae and Their Importance; 1.1.2 Brief History of Supernova Observations; 1.1.3 The Theoretical Perspective; 1.1.4 Aim; 1.2 Current Status of Supernova Observations and Modelling; 1.2.1 Traditional Supernova Types; 1.2.2 Observational Constraints on the Progenitors of Core-Collapse Supernovae; 1.2.2.1 Observables of Core-Collapse Supernovae; 1.2.2.2 Searching for SN Progenitor Stars; 1.2.3 Theory of Core Collapse Supernovae

1.2.3.1 The Collapse of a Typical Star1.2.3.2 Numerical Modelling; 1.2.4 Progenitor Dependence; 1.2.4.1 O-Ne-Mg Cores; 1.2.4.2 Iron Cores in Solar Metallicity Stars: Mass Dependence and Black Hole Formation; 1.2.4.3 Supernova Kicks and Binary Disruption; 1.2.4.4 Metallicity; 1.2.4.5 Rotation and Magnetic Fields; 1.2.4.6 Fast Rotation: Hypernovae, Long GRBs and Magnetic Field Amplification; 1.3 Challenges and Future Prospects; 1.3.1 New Supernova Types; 1.3.2 Multi-Messenger Astronomy; 1.3.2.1 Cosmic Rays; 1.3.2.2 Neutrinos; 1.3.2.3 Gravitational Waves

1.3.3 Challenges and Future Prospects from an Observational Point of View1.3.3.1 Progenitor Hunting; 1.3.3.2 Pre-SN Outbursts in SN Impostors/IIn SNe; 1.3.3.3 Flash Spectroscopy; 1.3.4 Future Prospects in Numerical Modelling; 1.3.4.1 Advances in High Performance Computing; 1.3.4.2 Subgrid Modelling; 1.3.4.3 Multidimensional Stellar Evolution; References; 2 Strongly Magnetized Pulsars: Explosive Events and Evolution; 2.1 Introduction; 2.2 Origin of the Magnetic Field; 2.3 Magnetic Field Evolution; 2.3.1 Hall and Ohmic Evolution; 2.3.1.1 Instabilities; 2.3.1.2 Cascades

2.3.1.3 Secular Evolution2.3.2 Magnetothermal Evolution; 2.3.3 Core Magnetic Field; 2.3.4 Magnetospheric Field; 2.3.5 Overview of Magnetic Field Evolution; 2.4 Explosive Events; 2.4.1 Bursts and Outbursts; 2.4.2 Giant Flares; 2.4.3 Timing Behaviour; 2.5 Persistent Emission and Spectral Features; 2.6 Magnetars and the Other NSs: The Top-Right Part of the P- Diagram; 2.7 Summary and Final Remarks; References; 3 Radio Pulsars: Testing Gravity and Detecting GravitationalWaves; 3.1 Introduction to Pulsar Timing; 3.2 Tests of Gravity with Radio Pulsars; 3.2.1 Testing Gravity with the PPK Formalism

3.2.1.1 Double Neutron Star Binaries3.2.1.2 Relativistic Spin Effects; 3.2.1.3 Best Test of GR: The Double Pulsar; 3.2.2 Testing Gravity Using the PPN Formalism; 3.2.2.1 SEP Violation and Orbital Dynamics; 3.2.2.2 SEP Violation: Violation of LLI and LPI; 3.2.2.3 Varying Gravitational Constant; 3.2.3 Tests of Alternative Theories of Gravity; 3.3 Gravitational Wave Detection with Radio Pulsars; 3.3.1 Detection Principle; 3.3.1.1 Generalization of the Residual Formula; 3.3.1.2 Stochastic Background; 3.3.2 GW Sources Relevant to PTAs and Their Signals; 3.3.2.1 Deterministic GW Signals; 3.3.2.2 Stochastic Backgrounds.