The Gay Science is a rambling mass of loosely connected pieces somewhat like the Jewish Wisdom literature in Proverbs or Ecclesiastes. It does not directly develop or converge, and it tries to be more honest to various moments and tropes than to any organizing theme or structure. Many of the segments are short dialog-format jokes.
The first English translator (Common) thought that this notion of 'science' was alien enough to ours, and enough closer to the usage in 'Wisdom Literature' that he translated it 'Wisdom' -- giving the work the title "Joyous Wisdom". But other choices he made were so bad that most folks now use a more literal translation throughout, including the title.
Literally, the word for science here is 'wissenschaft', and is formally parallel to the Greek word 'mathematike', both mean very generally 'rigorous techniques for handling knowledge', and neither corresponds narrowly to what we now think of as their modern synonyms. He also gives the title in Italian: 'La gaia scienza', capturing the fact that in other languages there is less of a 'doing of knowing' than just 'knowing' with the 'doing' left automatic.
One of the tropes early in the book is racial style, the distinction between Germanness, for instance, and Romanness or Greekness, even occasionally 'Orientalness', in the style of philosophy, law, morality or presentation. I think the choice of parallelism in verbiage here is significant from this point of view. What he is doing is 'that German thing', and maybe 'that Roman thing', but not 'that Greek thing'. Even if they are all thinking of what they are doing as the same sort of thing, they would disagree that they are actually doing anything alike. (At the same time, he works hard to escape from his own notion of 'Northernness', so it is a well-intended racism, and I think the intention is to emphasize relativism between cultures, not biology or tribal affiliation.)
Wissenschaft in German historically includes poetry, and Nietzsche makes a point of this by starting and ending the book with poems -- the introduction is in the form of something like drinking songs, and the final section is (slightly) more formal poetry. To me the argument being made seems to be to stretch the word's breadth and just stop being so fussy.