There is no universal agreement as to whether or not book titles should be underlined. Different style books address this issue in different ways; however, the major style books prefer that book titles not be underlined.
The Chicago Manual of Style states that book titles should be italicized and not underlined. The Modern Language Association has the same rule. However, the AP Stylebook dictates that book titles should have quotation marks around them. Other publications adhere by their own personal style guides, which may include underlining book titles. Sometimes, the best thing to do is to pick a style and just remain consistent with it.