Is a student's taking a classmate's book, with the intention of revenge after being subjected to bullying and assault, considered theft?

What this person is doing by mocking or physically assaulting is not permissible in Islamic law, for Allah Almighty says: ﴿O YOU WHO HAVE BELIEVED, LET NOT A PEOPLE MOCK [ANOTHER] PEOPLE﴾ [Al-Hujurat: 11], and the Prophet, peace and blessings be upon him, said: "Abusing a Muslim is a Fusuq (disobedience), and fighting him is disbelief," and "It is enough evil for a person to belittle his Muslim brother."

You have the right to claim your due from him, and if you are unable, you can seek redress from the concerned authorities. However, if you forgive and endure, you will be rewarded by Allah, for Allah Almighty says: ﴿BUT HE WHO PARDONS AND MAKES RECONCILIATION - HIS REWARD IS [DUE] FROM ALLAH﴾ [Ash-Shura: 40].

As for your stealing his book, it is a forbidden transgression, and what he did to you does not permit it, because permissible punishment is in proportion to the injustice, for Allah Almighty says: ﴿SO IF SOMEONE HAS ASSAULTED YOU, THEN ASSAULT HIM IN THE SAME WAY THAT HE HAS ASSAULTED YOU﴾ [Al-Baqarah: 194], and His saying: ﴿AND IF YOU PUNISH [AN ENEMY], THEN PUNISH WITH AN EQUIVALENT OF THAT WITH WHICH YOU WERE PUNISHED﴾ [An-Nahl: 126]. So, seek Allah's forgiveness and return his book to him. You may seek victory for yourself in the same way you were wronged, or you may forgive, and your reward is with Allah.