The description on YouTube does a pretty good job summarizing the programme here; it's based on Nietzsche's book of the same name ("Thus Spake Zarathustra"). The famous introductory theme, used in 2001: A Space Odyssey and as the unofficial theme music of the Apollo program (I don't know if they did that because of the Apollo-Nietzsche connection), consists of a perfect fifth and a perfect fourth--"C-G-C". It represents the sun rising and is repeated several times, most notably at the end of the sixth movement (starting subtly at 12:46 and clearly at 13:29), in which context it represents the apparent enlightenment bestowed by science. The sixth movement as a whole is particularly interesting, and provides the main connection with modernism. It represents, and maybe ridicules, science and empiricism through an egalitarian 12-tone melody. Treating all 12 tones equally, as previously noted, is a hallmark of the Austrian school of modernism, which (unfortunately for me trying to make connections) was not founded yet; however, we can maybe surmise that Strauss had heard people talking about atonality and thought he should lump it together with other useless, overly rational ways of thinking.
While Thus Spake Zarathustra is still fairly traditional, an example of Strauss's fully mature style is the Four Last Songs, written when he was 84, having accepted the role of aging conservative after being pretty forward-thinking through much of his middle period (if you're interested in Strauss's more avant-garde music, listen to his opera Elektra, which is more or less atonal). The last of them, Im Abendrot ("At Sunset") is based on a poem about death:
This was Strauss's last composition. It is pretty solidly a modernist piece; however, Strauss has abandoned the near-atonality of some of his earlier works. I like this kind of modernism much better than Schoenberg's: Strauss felt entirely free to violate traditional rules of tonality, but he did not shun tonality, instead recognizing it as a powerful tool to convey an impression.
The translates as:
gone hand in hand;
From our wanderings, let's now rest
in this quiet land.
Around us, the valleys bow
as the sun goes down.
Two larks soar upwards
dreamily into the light air.
Come close, and let them fly.
Soon it will be time for sleep.
Let's not lose our way
in this solitude.
O vast, tranquil peace,
so deep in the evening's glow!
How weary we are of wandering---
Is this perhaps death?
I think that the calm, joyful acceptance of death--and especially the reference to "solitude"--are very well conveyed by the music. Moreover, they reflect a more modern attitude of the kind we saw in Baudelaire.