Another great book on this topic is Rodney Stark's The Rise of Christianity https://www.amazon.com/Rise-Christianity-Marginal-Religious-Centuries/dp/0060677015/

Another great book on this topic is Rodney Stark's The Rise of Christianity https://www.amazon.com/Rise-Christianity-Marginal-Religious-Centuries/dp/0060677015/ref=sr_1_1?ie=UTF8&qid=1486480140&sr=8-1&keywords=the+rise+of+christianity https://www.amazon.com/Rise-Christianity-Marginal-Religious-... Stark is mostly interested in the period of time between Jesus and Constantine and brings a ton of historical and sociological evidence to bear on the question. A really amazing book. Learned a lot about Rome from it.