Table of Contents Preliminary 1.1. Common Sense 1.1.1. Units 1.1.2. Useful Conversions in Neutrino Physics 1.1.3. Diagrams 1.1.4. Refs and Notes 1.2. Physics 1.2.1. Reactions Related to Neutrinos 1.2.2. What is a Neutrino Particle? 1.2.3. Chirality and Helicity 1.2.4. Majorana or Dirac 1.2.5. States 1.2.6. Statistics 1.2.7. Refs & Notes 1.3. Mathematics Related 1.3.1. Pauli Matrices 1.3.2. The Equations 1.3.3. Equation Solving 1.3.4. Qualitative Analysis 1.4. Questions 1.4.1. Astrophysics Masses of Neutrinos 2.1. Theories of Neutrino Mass 2.1.1. Majorana Particle 2.1.2. Refs & Notes 2.2. Determine Neutrino Mass 2.2.1. Experiments Experiments 3.1. Neutrino Sources 3.2. Concepts in Experiments 3.2.1. Prediction of Theory 3.2.2. Sensitivity 3.2.3. Review of Experiments 3.2.4. Low Energy Neutrino Detection 3.2.5. Refs & Notes 3.3. List of Neutrino Experiments Oscillations 4.1. How Do Neutrinos Propagate 4.1.1. Wave Packet Treatment 4.2. Two-flavor and Three-flavor 4.2.1. Oscillation Scales 4.2.2. Refs & Notes 4.3. Evidence of Oscillations 4.3.1. Results of Experiments 4.3.2. Hamiltonian, Equation of Motion and Solution 4.3.3. Matter Effect - An Introduction 4.3.4. Q&A 4.4. Vacuum Oscillation 4.4.1. Survival Problem 4.4.2. Two Flavor States 4.4.3. The Standard Math for 2 Flavor Neutrino 4.4.4. Numerical Results for 2 Flavor Neutrino Oscillations 4.4.5. 3 Flavor Oscillations 4.4.6. Ternary Diagram 4.4.7. Understanding the Mixing Angles 4.4.8. Refs and Notes Interaction With Matter 5.1. MSW Effect 5.1.1. An Introduction to MSW Effect 5.1.2. Solar Neutrinos and MSW Effect 5.1.3. Numerical Results 5.1.4. Experiments 5.1.5. MSW Triangle 5.1.6. Refs and Notes 5.2. MSW Refraction, Resonance and Non-adiabacity 5.2.1. 2 Flavor Neutrino Oscillations and Matter Effect 5.2.2. Constant Electron Number Density 5.2.3. Adiabatic Limit 5.2.4. General Discussion of Matter Effect 5.2.5. Landau-Zener Transition of Neutrinos 5.3. Parametric Resonance 5.3.1. Parametric Resonance 5.3.2. Castle Wall Potential 5.3.3. Refs and Notes 5.4. Matter as Driven Energy 5.4.1. Oscillation in Matter and Vacuum 5.4.2. Rabi-like Transition 5.4.3. Analytical Attack 5.4.4. Period Matter Potential (NON-PHYSICAL) 5.4.5. Constant Matter with Periodic Perturbation 5.4.6. Resoances 5.4.7. Refs & Notes Collective Behavior 6.1. Collective Phenomenon 6.1.1. Spectral Split 6.2. Bipolar Model 6.3. Dense Homogeneous Isotropic Neutrino Gas 6.4. Refs & Notes Instability 7.1. Self-Interaction Instability 7.1.1. Linear Stability Analysis 7.1.2. Neutrino Self Interaction and Instability 7.1.3. Refs & Notes 7.2. List of Instabilities 7.2.1. Bimodal Instability 7.2.2. Multi-angle Instability 7.2.3. MAA 7.3. Bimodal Oscillations Pictures 8.1. Some Useful Physics Pictures 8.1.1. Magnetic Spin 8.1.2. Coupled Pendulum 8.1.3. Gyroscope or Spinning Top Picture 8.1.4. Polarization Vector 8.1.5. Neutrino-neutrino Interaction and BCS Theory 8.2. Flavor Isospin 8.2.1. Neutrino Flavour Isospin 8.2.2. Graphical Representation of Flavor Isospin 8.2.3. Refs & Notes Models 9.1. Homogeneous and Isotropic Neutrino Gas 9.1.1. What to expect? 9.1.2. Solving Eqns Statistical Physics 10.1. Neutrino Oscillation And Master Equation 10.1.1. Quantum Master Equation 10.1.2. Vacuum Oscillation Master Equation 10.1.3. Neutrino Oscillation in Matter - A Possible Master Equation Approach 10.1.4. Self Interaction Between Neutrinos 10.1.5. Refs & Notes Geometric Phase 11.1. Review of Geometric Phases 11.1.1. Berry Phase 11.1.2. Refs & Notes 11.2. Neutrino Oscillations and Berry Phase 11.2.1. Notes & References Astrophysics 12.1. Stars as Neutrino Factories 12.1.1. Neutrinos in Astrophysics 12.1.2. Solar Neutrino Spectrum 12.1.3. Neutrino Spectrum with Thermal and Relativistic Modifications 12.1.4. Supernova Neutrinos and Conclusion 12.1.5. Refs & Notes 12.2. Supernova 12.2.1. Neutrino Oscillations Gravity 13.1. Effect of Gravitation 13.1.1. Evaluation 13.1.2. Refs & Notes Neutrinos and Cosmology 14.1. Baryon Asymmetry in the Univserse 14.2. Cosmic Neutrino Background 14.2.1. Cosmic Neutrino Background 14.2.2. Refs & Notes Other Topics 15.1. Basis 15.1.1. Rotation of States 15.1.2. Rotation of Pauli Matrices 15.1.3. Rotation of Hamiltonian 15.1.4. Examples of Rotating Basis 15.1.5. Refs & Notes 15.2. Qualitative Analysis 15.2.1. Oscillation Period, Frequency and Energy 15.2.2. Refs and Notes 15.3. Neutrino Cheat Sheet 15.3.1. Refs & Notes 15.4. Frequently Asked Questions 15.4.1. Refs & Notes References Acknowledgement