I can speak to the history of the spread of Islam. I'll recommend a few books that I particularly value because they're concise (in about the 200ish page range).

I would check out Peter Brown's The World of Late Antiquity. It's perhaps a bit dated at this point but Peter Brown helped define "Late Antique" studies which covers roughly the period from when Christianity becomes a major force in the Roman empire up through the transition to the early medieval period with the rise of Islam. He's very good at establishing just how different that late antique/early medieval world was from our own which I think goes a long way to understanding the "rise of faith" as a major force in the greater Mediterranean world.

For the Islamic conquests themselves, Robert Hoyland's "In God's Path" is new, concise and pretty comprehensive history of the conquests. In terms of "bias" Hoyland has done some of the best work on using contemporary sources to try to resolve some of the objections raised by Patricia Crone (his teacher) and the other revisionists to get past the impasse produced by the lack of contemporary documentary Islamic sources in a way that I think is incredibly plausible.

As a third suggestion I would want to point you to something that covers a bit more of what those Islamic sources say about themselves which is to say the "traditional account." I'm personally highly skeptical of these accounts but they have to be understood to understand the religion. Pretty much anything you can get your hands on from W. Montgomery Watt would do you well as he represents sort of the high water mark of the traditionalists. His work "Muhammad Prophet and Statesman" is a concise example of this, to be contrasted strongly with something like Hoyland's essay Writing the Biography of the Prophet Muhammad: Problems and Solutions which I think is really important for understanding where the historiography stands on this.

In addition to /u/CptBuck's suggestions, I would add a book I'm reading now, Muhammad - Islam's First Great General by Richard A. Gabriel. As you can tell from the title, it's a socio-military history, as opposed to a religious history, and it raises some very interesting points about how Muhammad was so successful so quick at revolutionizing Arab society. It gives some background on Islamic beliefs in context with some preceding Arab cultural ideals and discusses some of the actual reforms Muhammad made and why. It also goes off on some very strange, irrelevant tangents on occasion and makes some very tenuous assumptions about Muhammad and his motivations, but overall I'd recommend it to anyone interested in understanding a bit more about the spread of Islam or early Islamic history. It's also very well sourced, which is always a plus.