Although it is prohibited to learn most Torah topics on Tisha B'Av, one may nevertheless study Eichah, sections of Jeremiah which relate to the Destruction and related Midrashim, the laws of Avelus (Mourning) and Ta'anis (Fasts), as well as Sefer Iyov (The Book of Job). (See Shulchan Aruch O.C. 554:1-3.) It is easily understood why most of the above texts are permitted to be learned on Tisha B'Av, as they deal with the Churban and sad occurrences. The rationale for permitting the study of Sefer Iyov, however, is somewhat of a mystery.
While it is true that most of Sefer Iyov addresses Iyov's suffering, there is seemingly nothing unique about the book which renders it appropriate for Tisha B'Av. Although most of the sefer addresses the plight of Iyov, its beginning and end address positive aspects of Iyov's life. By the same token, Tanach contains numerous other narratives about sad events, yet classical halachic literature does not note that these other texts may be studied on Tisha B'Av. What is it, then, about Sefer Iyov which makes it an appropriate text for the day on which we commemorate the Churban?
Aside from marking the anniversary of the destruction of the Beis Ha-Mikdash and Yerushalayim, as well as the exile of our people, Tisha B'Av represents the commencement of a long-term state of Hester Panim, which means that God "hides His Face" and is not readily perceptible to us in our everyday lives. Thus, inexplicable suffering endures, the righteous seem to be punished and the wicked appear to prosper, and open miracles which demonstrate God's control are almost unheard of anymore. Whereas before the Churban, we were guided by the Nevi'im (Prophets) who explained what Hashem was doing and why it had to be done, and God related to the universe in a manner which humans could comprehend, we are now in a post-Churban state of Hester Panim, unable to understand God's ways and subject to seemingly inexplicable circumstances. We know that Hashem is in control, yet we experience the fate of Hester Panim as originally prophesied by Moshe in the Tochachah (Rebuke) of Parshas Ki Savo and its narration in Parshiyos Vayelech and Ha'azinu.
This is precisely the link of Sefer Iyov to Tisha B'Av. Iyov's suffering was incomprehensible. At the end of the book, God speaks to Iyov and advises him that the ways of the Divine cannot be understood by Man. Hashem's works - whether they appeared to Iyov to be good or evil - are part of God's master plan and are mysterious to earthly beings, and one cannot question their legitimacy or wisdom. Only God, Who set up the cosmos and controls the fate of Man, knows the rationale behind why all things happen, and only He has mastery over all that transpires.
The story of Iyov enables us to understand what Hester Panim is all about. Just as Hashem spoke to Iyov and explained to him the state in which he found himself, Hashem likewise speaks to us through Sefer Iyov and intimates to us the character of Hester Panim, which was precipitated and is epitomized by Tisha B'Av.
So, too, among the Kinnos read on Tisha B'Av morning is the narration of the Asarah Harugei Malchus (10 rabbinic authorities who were martyred at the hands of the Romans). The beginning of this Kinnah features Rabbi Yishmael, the Kohen Gadol (High Priest), who invoked the Divine Name and was told from "On High" that the death of the Sages was a divine decree and could not be questioned. This is again part of the fundamental Hester Panim theme of Tisha B'Av, such that the righteous suffer and the wicked prosper, and we cannot understand why. It is at the core of Hester Panim, and is a basic principle in Judaism. (Avos 2:21, 3:19)
May we merit to soon again return to a state of Gilui Panim, in which we will understand God's plan for the world and be ever so close to Him once more.