Difference between καλός, αγαθός and χρηστός

Χαίρετε!

So far in Zuntz (lesson 4), he introduces these three words, but the only difference I can see is that Καλός seems to denote something that pleases the senses, instead of something necessarily good (Lesson 3, G1: Καλῶς λέγεις, φιλόσοφε), while χρηστός and αγαθός seem to mean a good thing, or a virtuous person (Lesson 3, F1: Χρηστοῦ ανθρώπου λόγος χρηστός. Lesson 4, A3: Πολλοὶ κακοί, ολίγοι δ`αγαθοί). Between these last two, I do not see anything at all that differentiates them. Are there any subtleties in meaning I am not getting?

Έρρωσθε!

Yes of course there are. Greek, like English, has very few exact synonyms. That said, χρηστός and αγαθός have a certain amount of semantic overlap; and καλῶς and εὖ have more. You could consult a lexicon, and observe usage.

I see. It seems these subtleties between synonyms really are the kind of thing that one only truly gets by assiduous observation of the language. Thanks!