1. Learning Torah on Tishah B’Av is prohibited because it causes the heart to rejoice as it states

 פקודי ה' ... משמחי לב.

2. Laws related to general mourning and Tishah B’Av are permitted to be learned. Texts related to tragedy such as Eichah, Iyob, Gemara discussing the Hurban, i.e. Gittin 56a-58, Sanhedrin 104, Yirmiyahu 32-40 (pesukim that talk about נחמה ,consolation should be skipped), Josephus.

3. Even thinking in learning is prohibited.

4. Children may only be taught material pertaining to the Hurban.

5. Even what one is permitted to learn cannot be learned in great depth, because it will bring simha.

6. Portions of the Torah recited in the prayers is permitted, however Tehillim and Hok L’Yisrael is prohibited.