Salafism

They mostly base their teachings off the Kutub al-Sittah, the Six Books, which are the Six authentic Hadith.

Wahhabism

The Reconstruction of Religious Thought in Islam by Muhammad Iqbal. Its used now for Islamic thought, and originally was written about previous Islamic philosophy. Wahhabism: A Critical Essay by Hamid Algar goes over Wahhabism a lot. The Principles of State and Government in Islam by Muhammad Asad talks about how an ideal Islamic society would work, and gives historical examples.

History

Destiny Disrupted: A History of the World Through Islamic Eyes by Tanim Ansary

As for battles and history during the time of the Muhammad, there are many Quranic commentaries that discuss that in chapters and verses.

Philosophy

Al-Madina al-Fadila by Al Farabi, basically the Islamic version of The Republic by Plato.

Sunni Shia Split/Jurusprudence

As for the split, there aren't much books outside of modern books that really talk about it directly, but you can read about the different ideas and laws between the sects.

As time passed, within 100 years after the death of Muhammad, there was the creation of Madhabs, schools of thought, which shape beliefs of Muslims now. Islamic jurisprudence/fiqh and Sharia go hand in hand, but fiqh is supposed to change depending on location, society, and time period, Sharia doesn't change.

There are four imams of Sunnism and one for Shii'ism

There is Imam Malik ibn Anas, who collected hadith regarding Islamic law and made Muwatta Imam Malik, and the commentary along with it is Mudawana.

Imam Malik taught one of the Imams, Imam Al-Shafi'. He was a governor also, of a Yemeni city. He wrote more than 100 books. Two of his books are most prominent in his school of thought/madhab, Kitab al-Umm and Al-Risala.

Next imam is Imam Abu Hanifa. He is the most widely followed Imam, mainly because the Ottoman empire used his fiqh. Fiqh al-Abasat and Fiqh al-Akbar are his books. However some scholars says it's not his books

Neither of them is a sound narration from Abu Haneefah (may Allah be pleased with him). Moreover, they both include opinions that are contrary to the view of Ahl as-Sunnah wa’l-Jamaa‘ah, as was explained by Dr. ‘Abd al-‘Azeez ibn Ahmad al-Humaydi in his book Baraa’ah al-A’immah al-Arba‘ah min Masaa’il al-Mutakallimeen al-Mubtadi‘ah, p. 46-71.

Imam Ahmad ibn Hanbal was probably the most controversial. He was the most conservative, known has Athari, and many scholars didn't accept his ideas of laws. Musnad Ahmad ibn Hanbal is his book.

Last Imam is Imam Jafar al Sadiq. He was the only Imam that was a direct descendant of Muhammad, and his ideas are followed by Shias. His teachers included Imam Abu Hanifa and Malik, both Sunni. A lot of Sunni scholars say that his works that have been attributed toward him have been corrupted in order to fit with Shia communities and such. He was also the one two have been attributed to have created the doctrine of Taqiyyah. His death caused turmoil among Shia. 4 groups split apart after his death because of disagreements in the next leader. He actually never wrote a book, but he did teach jurisprudence to his students, and his father had a book too.

This [website] (https://www.al-islam.org/the-origins-and-early-development-of-shia-islam-sayyid-jafari) has a lot of good information on Shia times and development. Sunni is basically everything else, including Sufism.

Kimiya-yi sa'ādat by Al Ghazali is a good book about the basics of Sufism and gives a lot of insight on why it was attractive to people back then