Father Sergius, by Leo Tolstoy

Very enjoyable and thought provoking story about a young Russian nobleman and military officer who is disillusioned by human weakness, vice, and sin in the world and decides to give up a brilliant military career to become a priest.  He discovers to his chagrin that sin and weakness have a long reach. They continue to bedevil him even as a priest in a big city, then even as a hermit in a remote monastery.  His search for spiritual improvement does not prove fruitless, however, because he realizes what his most insidious fault is when he abandons his hermitage in shame after a serious lapse and visits an old childhood friend in reduced circumstances.     

I suspect this story may have been inspired by Tsar Alexander I, who was rumored to have faked his death and entered a monastery, living the rest of his life under an assumed identity.