The Gemara of Shabat establishes a number of restrictions on reading material on Shabat, including a prohibition against reading words written underneath a picture of a painting. Chachamim forbade reading these words as a safeguard against reading commercial documents and the like, which is clearly forbidden on Shabat.
Rabbi Moshe Halevi, in his sefer, “Menuchat Ahavah,” cites various Rabanim who allow reading on Shabat the captions underneath pictures of Rabbis. Since there is a mitzvah involved in looking at pictures of distinguished Rabbis, as this could enhance one’s Yirat Shamayim, it would be permitted to read the captions identifying the Rabbis, even on Shabat. Nevertheless, Rabbi Moshe Halevi advises conducting oneself stringently in this regard, and refraining from reading even the captions underneath pictures of great Rabbis.
Halachah forbids proofreading material on Shabat, as well. Likewise, a Sofer (scribe) may not review a Sefer Torah on Shabat, even though he of course plans to correct any mistakes only after Shabat.
It is forbidden to read advertisements on Shabat, even if they pertain to mitzvah merchandise or services, such as advertisements for Judaica, books of Torah or Arba Minim (four species).
It therefore goes without saying that reading novels, science fiction, newspapers and other mundane material is forbidden on Shabat. One’s reading during Shabat should be devoted exclusively to the study of Torah.