Xuan (玄, Mystery) in the Dao De Jing: Meaning and Occurrences
In the Dao De Jing, xuan (玄) means dark and mysterious: it marks what cannot be seen into, from the "mystery within mystery" of chapter 1 to the mysterious virtue of chapters 10, 51 and 65.
玄 (xuán) first names a color, a deep black with a tinge of red, and from there came to mean dark, deep and hard to see into. This site translates it "mystery" or "mysterious".
Chapter 1 ends with it: the two that come out together are both called mystery, "mysteries within mysteries", the gateway to all marvels. Chapter 6 says the spirit of the valley does not die and calls it "the mystic female" (玄牝).
Most other uses are set phrases. 玄德, "mysterious virtue", ends chapters 10 and 51 and returns in chapter 65; 玄同, "mysterious oneness", is in chapter 56. Chapter 10 also has 玄览, and chapter 15 describes the ancient masters as subtle, marvelous and mysteriously penetrating (玄通).
Every occurrence of 玄
Chapter 1
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Line 8
同谓之玄，玄之又玄，
Both are considered mysteries, mysteries within mysteries,
Chapter 6
Chapter 10
Chapter 15
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Line 1
古之善为士者，微妙玄通，深不可识。
The ancient masters of the Way had subtle marvelous mystic penetration; a depth that cannot be known.
Chapter 51
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Line 11
是谓玄德。
This is called mysterious virtue.
Chapter 56
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Line 4
是谓玄同。
this is called mysterious oneness.