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The SLAC Summer Institute (SSI) is an annual two-week-long Summer School tradition since 1973. Given the special circumstances and uncertainties with COVID-19 continuing this year, we are planning for a reduced program of just three online lectures each morning through the two weeks, without the usual afternoon programs in regular editions. We still require interested participants to register online (no registration fee) in order to receive updated online instructions. SSI is especially targeted for graduate students and postdocs while senior researchers are also welcome. 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.