Compact Stars -- DYNAMIC STABILITY OF COMPACT STARS -- CONSTRAINTS ON SUPERDENSEMATTER FROM X-RAY BINARIES -- POSTGLITCH RELAXATIONS OF ANGULAR VELOCITY OF PULSARS -- ISOLATED NEUTRON STARS: AN ASTROPHYSICAL PERSPECTIVE -- Superdense QCD Matter -- CLUSTERS AND CONDENSATES IN THE NUCLEARMATTER EQUATIONOF STATE -- NUCLEAR EQUATION OF STATE AND THESTRUCTURE OF NEUTRON STARS -- NEUTRON STAR STRUCTURE WITH HYPERONS AND QUARKS -- THE QCD EQUATION OF STATE AND QUARK STAR PROPERTIES -- EFFECTIVE LAGRANGIANS FOR QCD: DUALITY AND EXACT RESULTS -- COLOR SUPERCONDUCTIVITY AND HIGH DENSITY EFFECTIVE THEORY -- COLOR SUPERCONDUCTING QUARK MATTERAND THE INTERIOR OF NEUTRON STARS -- SUPERCONDUCTIVITY WITH DEFORMED FERMI SURFACES AND COMPACT STARS -- NEUTRAL DENSE QUARK MATTER -- POSSIBILITY OF COLOR MAGNETIC SUPERCONDUCTIVITY -- MAGNETIC FIELDS OF COMPACT STARS WITH SUPERCONDUCTING QUARK CORES -- THERMAL COLOR-SUPERCONDUCTING FLUCTUATIONS IN DENSE QUARK MATTER -- THE INNER STRUCTURE OF HYBRID STARS -- Signals for Superdense QCD Matter in Compact Stars -- GAMMA-RAY BURSTS AND THEIR CENTRAL ENGINES -- SUPERDENSE STARSWITH A QUARK CORE -- DIQUARKCONDENSATION EFFECTSON HOT QUARK STAR CONFIGURATIONS -- GAMMA RAY BURSTS AND DELAYED QUARK-DECONFINEMENT -- COLOR SUPERCONDUCTING QUARK MATTER AND COMPACT STAR OBSERVABLES -- LOOKING INSIDE THE EARTHWITH SOLARAND SUPERNOVA NEUTRINOS: AN ANALYTIC APPROACH -- DECONFINEMENT PHASE TRANSITION IN RELATIVISTIC NEUTRON STAR MERGERS.

2 Homogeneous superconducting state 210 3 Superconducting phases with broken space symmetries 213 4 Flavor asymmetric quark condensates 219 5 Concluding remarks 221 Acknowledgments 222 References 223 Neutral Dense Quark Matter 225 Mei Huang and Igor Shovkovy 1 Introduction 225 2 Local charge neutrality: homogeneous phase 226 3 Global charge neutrality: mixed phase 234 4 Conclusion 238 References 238 Possibility of color magnetic superconductivity 241 Toshitaka Tatsumi, Tomoyuki Maruyama, and Eiji Nakano 1 Introduction 241 2 What is ferromagnetism in quark matter? 243 3 Color magnetic superconductivity 248 4 Chiral symmetry and magnetism 253 5 Summary and Concluding remarks 258 Acknowledgments 260 References 260 Magnetic Fields of Compact Stars with Superconducting Quark Cores 263 David M. Sedrakian, David Blaschke, and Karen M. Shahabasyan 1 Introduction 263 2 Free Energy 265 3 Ginzburg-Landau equations 267 4 Vortex Structure 269 5 Solution of Ginzburg-Landau Equations 271 6 The Magnetic Field Components 273 7 Summary 275 Acknowledgments 275 References 275 Thermal Color-superconducting Fluctuations in Dense Quark Matter 277 D. N.