What are the most sacred of the High Holy Days during the Jewish religious year?

What most people fail to grasp is that the Sabbaths (weekly and Annual) do not belong to Jews or Hebrews or Gentiles. They are God's and you may read of them in Leviticus 23.

Leviticus 23New International Version (NIV) Leviticus 23

The Appointed Festivals1 The LORD said to Moses, 2 "Speak to the Israelites and say to them: 'These are my appointed festivals, the appointed festivals of the LORD, which you are to proclaim as sacred assemblies

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The Sabbath

3 "'There are six days when you may work, but the seventh day is a day of sabbath rest, a day of sacred assembly. You are not to do any work; wherever you live, it is a sabbath to the LORD.