Textbook in cosmology covering established and speculative research for advanced students of physics and astrophysics.This textbook takes an original approach to cosmology by showing where theoretical results come from, in addition to discussing the basis of modern cosmology. The book covers established material as well as bringing the reader to the frontiers of current cosmological research by the discussion of more speculative ideas. An ideal textbook for advanced students of physics and astrophysics, all of the necessary back ground material is included in every chapter and no prior knowledge of general relativity and quantum field theory is assumed.This textbook takes an original approach to cosmology by showing where theoretical results come from, in addition to discussing the basis of modern cosmology. The book covers established material as well as bringing the reader to the frontiers of current cosmological research by the discussion of more speculative ideas. An ideal textbook for advanced students of physics and astrophysics, all of the necessary back ground material is included in every chapter and no prior knowledge of general relativity and quantum field theory is assumed.Inflationary cosmology has been developed over the last twenty years to remedy serious shortcomings in the standard hot big bang model of the universe. Taking an original approach, this textbook explains the basis of modern cosmology and shows where the theoretical results come from. The book is divided into two parts; the first deals with the homogeneous and isotropic model of the Universe, the second part discusses how inhomogeneities can explain its structure. Established material such as the inflation and quantum cosmological perturbation are presented in great detail.Part I. Homogeneous Isotropic Universe: 1. Kinematics and dynamics of an expanding universe; 2. Propagation of light and horizons; 3. The hot universe; 4. The very early universe; 5. Inflation I: homogeneous limit; PalĂ`