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In 2012 the Higgs boson (the Higgs particle) was discovered at the LHC (Large Hadron Collider) at CERN (European Organization for Nuclear Research) in Switzerland. The existence of the Higgs boson has been firmly established by numerous experiments since then. In the standard model of particle physics the Higgs boson had been the last piece to be found in addition to leptons, quarks and gauge bosons. The discovery of the Higgs boson, besides being the discovery of a new particle, has profound implications to particle physics. It is often said in the news media that the Higgs boson explains the origin of masses in the universe. This is quite misleading. Most masses of matter which we see in our daily life are explained in terms of the mass of protons and neutrons. It is known that only 2% of the mass of protons and neutrons is due to the Higgs boson. The rest is generated by strong interactions. This fact had been pointed out by Y. Nambu before P. Higgs proposed his theory. The importance of the discovery of the Higgs boson lies in a different place. The Higgs boson is absolutely necessary in the standard model in which electromagnetic and weak forces are unified. In order for two distinct forces to be unified in a single force, one needs a mechanism by which one force differentiates into two distinct forces at low energies. The Higgs boson plays an essential role in this process. In other words, the discovery of the Higgs boson has established the scenario of the unification of forces. However, we still do not have good understanding of what the Higgs boson is. From the mathematical point of view, the process of a single force differentiating into two distinct forces is a process in which gauge symmetry partially breaks down spontaneously. The Higgs mechanism is a mechanism for spontaneous gauge symmetry breaking, and is employed in the standard model. The details of the mechanism are yet to be explored experimentally. There is another mechanism for spontaneous gauge symmetry breaking. It is the Hosotani mechanism in which gauge symmetry in four-dimensional spacetime is spontaneously broken by dynamics of the fifth-dimensional component of gauge fields. The mechanism is the generalization of the Aharonov-Bohm effect in quantum mechanics to the fifth dimension. The Higgs boson appears as a four-dimensional fluctuation mode of Aharonov- Bohm phases. Gauge fields and the Higgs boson are unified, thus the scenario being termed gauge-Higgs unification. The interaction of the Higgs boson is controlled by the gauge principle. The finite mass of the Higgs boson is generated by quantum effects. The Hosotani mechanism was discovered in 1983. At the time it was difficult to describe the chiral nature of the weak interactions of quarks and leptons, and no realistic models were constructed. Since then good progress has been made in field theory on orbifolds and the Randall-Sundrum warped space. In the 2010’s realistic gauge-Higgs unification models have become available. In this book the Hosotani mechanism and gauge-Higgs unification scenario are explained from the basics. The book is intended both for advanced undergraduate and graduate students, as well as for frontier researchers. Minimal knowledge of field theory is assumed. After reviewing the Higgs mechanism and the standard model in Chapter 2, we introduce the Hosotani mechanism in Chapter 3 which generalizes the Aharonov-Bohm effect to non-Abelian gauge theory. The effective potential is introduced in Chapter 4, with which we see how dynamical gauge symmetry breaking occurs by the Hosotani mechanism. Gauge symmetry breaking on the lattice is also examined. In Chapter 5 general properties of field theory in higher dimensions are reviewed. In addition to the universal extra dimension model, we examine a few gauge-Higgs unification models on the flat M4 ×(S1/Z2) orbifold. Difficulties in having realistic gauge-Higgs unification models on flat orbifolds are recognized.