In an essay from 2013, Aaron Ross Powell describes libertarianism, succinctly and well:
In medical ethics, there’s the principle primum non nocere. “First, do no harm.” It’s one libertarians keep very much in mind when approaching politics. Most government “solutions” don’t simply not work. They actually make things worse than if they hadn’t been enacted at all. Thus standing in opposition to expanded government isn’t motivated by an uncaring attitude about America’s problems. Instead, it’s motivated by a well-founded understanding of how often government is the cause of those problems….
What we offer is not some powerful man in Washington directing the country, but freedom. Which means freedom for Americans to do unpredictable things. Our solutions are based in the knowledge that many of those unpredictable things (many of the outcomes of unleashed market forces, for example) will radically improve the lives of nearly everyone touched by them….
Libertarianism is an ideology of respect—for people, for their choices, for their values and desires. It is an ideology of hope, one that sees a path to a much better future. Even if that path isn’t as precisely drawn as some might like.
See, in full, First, Do No Harm @ Libertarianism.org.