One is not allowed to learn Torah on Tisha B'Av, as it gladdens a person (SA 554:1-2). However, certain texts, relating to mourning and the destruction of the Beis HaMikdash, are permissible (Mishnah Berurah ad. loc.).
What about texts that describe what happened in the Beis HaMikdash - Seder Kadshim, Masechtos Shekalim and Chagigah, etc. (or at least the on-topic parts)? Is the list provided in the Mishnah Berurah an extensive list, or is it just a list of examples of that which one may learn?
The answer is written in Gemara and Poskim:
Our Rabbis have taught: All the restrictions that apply to the mourner hold equally good of the Ninth of Ab ... It is also forbidden [thereon] to read the Law (Pentateuch) {they rejoicing the hearth}, the Prophets, and the Hagiographa or to study Mishnah, Talmud, Midrash, Halachoth, or Aggadoth; he may, however, read such parts of Scripture which he does not usually read and study such parts of Mishnah which he usually does not study {he is not so good at understanding and is suffering}; and he may also read Lamentations, Job and the sad parts of Jeremiah; and the school children are free from school for it is said, The precepts of the Lord are right, rejoicing the heart. [These are the words of Rabbi Meir] {version of the Rif, Rosh and Or Zarua (annotation from the Gra)}.
R'Judah said: Even such parts of Scripture which he does not usually read he may not read, nor study parts of the Mishnah which he does not usually study {because that after the hardness of the study will become the happiness of understanding Torah (Taz OC 524, sk 2)}, but he may read Job, Lamentations and the sad parts {sad for Jews, not sad for Nations, poskim} of Jeremiah; and the school children are free [from school] for it is said, 'The precepts of the Lord are right, rejoicing the heart'.
Rambam Zemanim, Taanit, Chapter 5, Halacha 11 stated for stringency as Rabbi Yehuda about text which he doesn't usually read:
On Tish'ah B'Av, it is forbidden to read from the Torah, the Prophets, or the Sacred Writings [or to study] the Mishnah, Torah law, the Talmud, or the Aggadic works. One may study only Job, Eichah, and the prophecies of retribution in Jeremiah. Children should not study in school on this day.
The Shulchan Aruch adds in Orach Chayim, 554:2:
Midrash Eicha, Perek Velu Megalchim (3rd of Massechet Moed Katan), commentaries on Eicha and Yiov
Saif 3: Some Poskim prohibited the prohibited studies in thinking, not only in speaking, because thinking Torah give also a pleasure.
Saif 4: We can read Seder Hayom, Korbanot, Eizehu Mekoman (3ts of Zevachim)
In Mishna Berura sk 2 you can find also Agadot Hatalmud about the destruction of the Temple: in Gittin perek Hanizakin, in Sanhedrin Perek Chelek, Josephus.
I hope that this answer is valuable.
