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This is a pedagogical introduction to the physics of confinement on $R^3\times S^1$, using $SU(2)$ Yang-Mills with massive or massless adjoint fermionsas the prime example; at the end, we also add fundamental flavours. Thesmall-$S^1$ limit is remarkable, allowing for controlled semiclassicaldetermination of the nonperturbative physics in these, mostlynon-supersymmetric, theories. We begin by reviewing the Polyakov confinementmechanism on $R^3$. Moving on to $R^3 \times S^1$, we show how introducingadjoint fermions stabilizes center symmetry, leading to abelianization andsemiclassical calculability. We explain how monopole-instantons and twistedmonopole-instantons arise. We describe the role of various novel topologicalexcitations in extending Polyakov's confinement to the locally four-dimensionalcase, discuss the nature of the confining string, and the $\theta$-angledependence.~We study the global symmetry realization and, when available,present evidence for the absence of phase transitions as a function of the$S^1$ size. As our aim is not to cover all work on the subject, but to preparethe interested reader for its study, we also include brief descriptions oftopics not covered in detail: the necessity for analytic continuation of pathintegrals, the study of more general theories, and the 't Hooft anomaliesinvolving higher-form symmetries.

Notes on Confinement on $\mathbf{R^3 \times S^1}$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)