Learn Russian: Весь космос — это тайна.

Весь is the masculine singular form meaning "all" or "the whole." It must agree with the gender of the noun it modifies, which in this case is the masculine noun космос (space). You would use всё for neuter nouns (or for "everything") and все for plural nouns (or "everyone").

Does весь mean "all of" or "the whole"?

It can mean both! Depending on the context, весь translates to "all of," "the whole," or "the entire." Here, "The whole of space" or "The entire cosmos" would also be perfect English translations.

Why is there a dash and the word это before тайна?

Russian usually drops the verb "to be" (is/are) in the present tense. When equating two nouns (like "space" and "mystery"), Russians often use a dash and the word это to bridge them. The structure literally translates to "All of space — this [is] a mystery."

Since тайна comes after the "is" concept, does it change its case?

No, тайна stays in the nominative (dictionary) case. When using this "[Noun 1] — это [Noun 2]" structure, both nouns remain in the nominative case because the sentence is simply stating that one thing equals the other.