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The 2021 SLAC Summer Institute will focus on the physics of the Higgs sector, from its foundational role in the Standard Model to the various Beyond the Standard Model scenarios, as well as its cosmological connections. Several aspects of spontaneous symmetry breaking are not yet well understood and many properties of the 125 GeV Higgs boson are either poorly determined or remain unmeasured. Some fundamental assumptions in most existing investigations also require more concerted probing. Through future measurements, these poorly known aspects of the Higgs may lead to new opportunities to explore for new physics signals such as links to the dark sector and/or long-lived particles, as well as to unexpected flavor dynamics and/or new sources of CP-violation. The lectures are primarily aimed at senior graduate students and postdocs. 2021 SLAC Summer Institute will focus on a broad spectrum of topics associated with the Higgs.