Read beyond your comfort zone
Just about anytime you bring up the subject of libertarian books and authors, someone will mention Ayn Rand's "Atlas Shrugged". That's OK, and I do enjoy the book- even the infamous monologue- while pointing out that it is not specifically libertarian. I will admit it has inspired a lot of people to shift their world-view in a more libertarian direction, though.
Most people seem to think "Atlas Shrugged" is too preachy, and many like to focus on Rand's personal shortcomings rather than stay focused on the book. For those people, and the rest of us, it's a good thing there are so many other libertarian books that are a lot more fun to read.
If fiction is your preference, you might like "Hope" by Aaron Zelman and L. Neil Smith, which looks at what might happen if a real libertarian ever found himself elected president. It's a fun story!
If you are a younger reader you might enjoy "Out of the Gray Zone" by Claire Wolfe and Aaron Zelman which follows the adventures of a young escapee from a totalitarian society.
Many books by science fiction authors H. Beam Piper and Robert A. Heinlein have a strong libertarian streak. In fact, most science fiction either tends to be either highly collectivist in nature or very libertarian. Perhaps because science fiction explores the extremes.
Lying between fiction and non-fiction is "A Vision of Liberty" by Jim Davies. Mr. Davies lays out his vision of a free society looking back at the end of government.
For non-fiction readers there are also plenty of options.
In "How I Found Freedom in an Unfree World" by Harry Browne, this liberty activist and former Libertarian Party presidential candidate describes his personal experiences living a free life while surrounded by people who don't appreciate freedom.
If Browne's ideas inspire you, you might like "The Freedom Outlaw's Handbook" by Claire Wolfe. In it you'll find 179 things you can do to protect and increase your individual liberty now, and have fun, while confounding those who would prefer to see you enslaved to one degree or another.
Of course you shouldn't limit your reading to only things that you agree with. See what the other side has to say. It is fun to read random fiction and, for example, see where the characters went wrong and how they could have avoided problems by not initiating force. Or think of ways you could have solved their Big Problem without violating the rights of any of the other characters. As always, worthwhile reading exercises the mind.
And please don't forget.