Yes, you will italicize book titles when writing in MLA style, both in the citation and anywhere you might mention the title in your work.
However, if you're referring to a chapter title within a book, that will go inside "quotation marks."
Other works that get italicized:
- Report names
- Movie titles
- Painting titles
- Newspaper & magazine titles
- Website names
- Library database names
- Anything that is a large whole work, complete in and of itself.
What about underlining?
Underlining is used when italics aren't possible -- e.g. when you're handwriting, you'll probably underline a book title rather than try to write in italics. Underlines are not recommended when typing, because in digital content, the underline indicates a link.
Another alternative to italics is ALL CAPS for a work title. You'll see this occasionally with book publishers. Don't do this in your essays, though.