Amelia is the story of a young couple at the beginning of their marriage and the issues they have to work through together. Forbidden by her mom to marry him, Amelia falls in love with Booth all the same. They get married and run off to London together. Then, tragedy hits as he's wrongly imprisoned.
Their marriage is not a healthy one throughout the book. Granted, they aren't faced with the normal problems of a married couple: wrongful arrest, massive debt, infidelity, tragic accidents, and family deaths. They work through these things, making mistakes and amends respectively along the way. Basically what happens over and over is that Booth chooses the wrong thing, hurting the marriage. Then, Amelia saves him until finally her mom dies.
Amelia inherits her mom's estate, and they are able to essentially restart their lives with some money in the country. The story is one of continuous grace and devotion. Despite Booth's faults, Amelia loves him, and together they work through their problems to build a healthy relationship.