2. Mutated and smooth hybrid inflation 84 3. Shifted and other variants of hybrid inflation 86 4. Assisted inflation 88 5. Non-Gaussianities from multi-field models 90 6. Challenges for non-SUSY models 92 D. SM Higgs as the inflaton 95 1. Dynamics of the SM Higgs inflation 95 2. SM Higgs inflation and implications for collider experiments 97 E. SUSY models of inflation 98 1. Chaotic inflation in SUSY 99 2. Hybrid inflation from F -terms 100 3. CMB predictions and constraints 101 4. SUGRA corrections to F -term inflation 103 5. Non-minimal kinetic terms and the SUGRA η problem 104 6. Initial conditions for F -term hybrid inflation 106 7. Other hybrid models and effects of non-renormalizable terms 107 F. Inflation from D -terms in SUSY and SUGRA 114 1. Minimal hybrid inflation from D -terms 115 2. Constraints from CMB and cosmic strings 117 3. D -term inflation from superconformal field theory 119 4. D -term inflation without cosmic strings 120 5. F$_{D}$ -term hybrid inflation 123 6. Embedding D -term models in string theory 125 7. Hybrid inflation in N = 2 SUSY: P -term inflation 127 G. Embedding inflation in SUSY GUTs 128 1. Inflation in non-SUSY GUTs 129 2. Hybrid inflation within SUSY GUTs and topological defects 131 3. Embedding inflation within GUT 133 4. Origin of a gauge singlet inflaton within SUSY GUTs 135 5. Other inflationary models within SUSY GUTs 137 6. Inflation, neutrino sector and family replication 140 4