Reddit mentions of Muhammad: A Very Short Introduction

Just noted this part of your reply.

>it's his claim that compared with Jesus, the amount of genuine scholarship on the historicity of Mohammed is woefully lacking.

What are you talking about? There are scholars for the revisionist theory, albeit outdated. John Wansbrough, Patricia Crone, Joseph Schacht, Michael Cook. The ones that I'm fond of and they all have impeccable credentials (the number of degrees, and where you obtained them from actually do matter) Fred Donner, Harald Motzki, Jonathon Brown, and Andreas Goerke.

I usually recommend these two books to anyone that's interested in the history of Muhammad and Islam, they're critical of the traditional narrative among others.

Muhammad And The believers: At The Origins of Islam by Fred Donner

Muhammad: A Very Short Introduction by Jonathon Brown

https://www.amazon.com/Muhammad-Introduction-Jonathan-C-Brown/dp/0199559287

You asked for everything really, but here is a selection I personally like that is more focused on the biography of Muhammad.

For Muslim books on the biography of the Prophet, I highly recommend:

A Biography of the Prophet of Islam: In the Light of the Original Sources, an Analytical Study

In the Footsteps of the Prophet: Lessons from the Life of Muhammad

Muhammad: His Life Based on the Earliest Sources

On the more academic side of his life and following centuries, I recommend:

Muhammad: A Very Short Introduction

Hadith: Muhammad's Legacy in the Medieval and Modern World

In God's Path: The Arab Conquests and the Creation of an Islamic Empire

The Death of a Prophet: The End of Muhammad's Life and the Beginnings of Islam

For the four best primary sources of his biography translated into English:

The Life of Muhammad: Al-Waqidi's Kitab al-Maghazi

The Life of the Prophet Muhammad: Al-Sira al-Nabawiyya

The Life of Muhammad

The Expeditions: An Early Biography of Muhammad

I recommend John Brown's Muhammad - A Very Brief Introduction. The biographic tradition of Muhammad is highly controversial, and after Brown introduces the biography, he explains why it's inauthentic. For example, there was no massacre of Jews, Satan never tricked Muhammad to recite his verses instead of the Quran, and many other stories the first biographer plagiarized from Jewish and Christian lore.