This book investigates the physics of the discovered Higgs boson and additional Higgs bosons in the extended Higgs models which includes higher-order quantum corrections. While the 125 GeV Higgs boson was discovered, the structure of the Higgs sector is still a mystery. Since the Higgs sector determines the concrete realization of the Higgs mechanism, the study of its nature is one of the central interests in current and future high-energy physics. The book begins with a review of the standard model and the two-Higgs doublet model, which is one of the representatives of the extended Higgs models. Subsequently, we discuss the studies of the two-Higgs doublet model at the lowest order of perturbation. Following the lowest-order analysis, we study the higher-order electroweak corrections in Higgs physics. After reviewing the renormalization procedure and the higher-order corrections in the decays of the discovered Higgs boson, we discuss the higher-order corrections in the Higgs strahlung process from an electron-positron collision, the decays of the additional charged and CP-odd Higgs bosons in the two-Higgs doublet model. From the series of these studies, it is found that the nature of the Higgs sector can be widely investigated by future collider experiments.