This is a classic sci-fi story with strong religious theme and setting. 
 After a nuclear war the world is a wasteland, like so many past dictators those that survive push their anger towards the educated. An order of the the Catholic church has taken on the task of preserving man's scientific knowledge until society is again ready for it. This is the story one monastery order that takes on this task for thousands of years. 
 The book is broke into three stories: The first a novice monk, who is prone to fainting, makes a discovery that unwillingly involves him in the canonization process of the order founder Leibowitz. We see how the monks offer their work and preserve the past. In the second story, civilization has advanced to a new renaissance age and a leading secular scientist comes to the monastery to review and discover the history and scientific knowledge they have kept. The third story takes place when society have advanced to the stars but is on the verge of destroying itself, again. The church takes steps to not repeat the past and give the future hope, we also see how people react to suffering. 
 The characters are well realized. These are not cloistered monks that do nothing but pray. They're normal people with humour and personalities, who have devoted their life to their work and their faith. It also does not water down religious teaching or try to 'modernize' it. Often authors will adjust the church teaching to show so call progress, that is not the case here. The Abbots fight against euthanasia is as strong as someone today would be. 
 Since it was written in the 1960s the technology referenced can feel dated, there no computers, which may be a good thing for preserving knowledge. The world is well realized but may seem cliche to people despite it being one of the first. 
 Explores themes of technological vs social development, history repeating itself, and church vs. secularism. Give hints of events that can be either interpreted as divine, as often is by the POV, or explained by other means by the reader if they so chooses. 
 Worth reading if you like classics, somber but funny post-apocalyptic stories or religious and philosophy themes. You don't have to be catholic to appreciate it but you'll appreciate the through and detail the author put into it.