This looks like a good place to start if you just want a general history. But it's not a book:
But I suspect the Jains may have been the first to have a monastic tradition. And since Judaism isn't supportive of monasticism, I've always wondered if Christian monasticism didn't have some contact with Buddhist monasticism as a model. So you may have to look at religions that pre-date Christianity if you're interested in the history of monasticism in the general sense. Of course, I'm not a historian or theologian, so I could be wrong about this.
I think this theory that the Christians learnt from the Jains would be very difficult, in not impossible, to substantiate and that from what we do know of history it would require a great deal of substantiation to become credible. Further, I'd like to know what points of Jainism you consider correspondent to what points in Christian monasticism?
As for the Jews, they had vowed members of the congregation such as Nazarites from a very ancient period. Further, there is much in ancient Judaism as a whole to inspire a special mode of life. The entire congregation of Israel was "set apart" a "peculiar people" to whom was spoken by Jehovah himself: "Come ye out from among them [i.e., the world] and touch not the unclean thing." When the Jews were discovered by the Greeks, their reputation as a nation of great erudition and piety spread rapidly and earned them the name "the nation of philosophers" of whom one chronicler wrote, "Even their women and children are philosophers." If we look at the sects of the Pharisees or Essenes, the types of Judaism prominent at this period, we see different sorts of what is still in both cases, compared to the world, a very purposeful practical piety of everyday life not unlike monasticism. Finally, consider the priests and Levites and their many special prescriptions according to the Law.
In the end, because what monasticism offers corresponds to what the human condition needs, it was inevitable by Spirit and nature that something like monasticism arise in the religion of the "God who alone loves humankind," as well as, to some lesser and corrupted extent, in other serious religions. Monasticism as it came to us was woven of many historical threads. The Mosaic influence I have already touched on. The Gospel of Christ and Apostles taken peculiarly to heart is another -- and all the early hermits and the Fathers who dealt with monasticism express this fact clearly and thoroughly. The influence of Plato is also alleged. Let me conclude by again pointing out that it is a true and reliable answer to all questions about the Church thru the ages that the Holy Spirit is able and willing to "teach [her] of all things" -- i.e., that there really is a means by which Heaven can teach those on earth who listen.