If I had the power to persuade non-libertarians to read one book right now I’d choose The Problem of Political Authority by Michael Huemer. It's a distillation of the most robust and compelling arguments against the legitimacy of the state I’ve come across in ten years of exploring the topic.
If you don’t self-identify as a libertarian before reading this with an open mind I wouldn't be surprised if you do three months after finishing it. At the very least you’ll have gained an appreciation for the most powerful arguments for libertarianism and you can truthfully say you gave the idea a fair chance.
If you already self-identify as a libertarian the book is valuable too. As well as rebutting a greater breadth of pro-state and anti-anarchy arguments than I’ve seen collected elsewhere, it’s a great illustration of the value of defending anti-statism by relying on the reader’s desire for coherence in their moral judgements. The author begins by finding common ground with the reader: agreement about the conditions under which the interpersonal use of violence is condemnable. He proceeds by carefully examining each of the strongest attempts to show that the state’s use of violence is different in some ethically significant way to the violence that we condemn. All the arguments examined are demonstrated to be insufficient to the task of rescuing the state from our condemnation.
The arguments challenging the state's legitimacy never depend on the reader accepting a controversial premise (such as the existence of natural rights, or of free will, or the truth of a particular ethical theory). This is the same approach I tried to take with my George Ought to Help series of animations.
The chapter on the The Psychology of Authority is particularly interesting to me. Huemer examines well-documented cognitive biases to provide an account of why so many people are in thrall to a cognitive illusion (the belief in the right of the state to coerce) that’s at odds with their foundational moral intuitions.
The second part of the book is dedicated to outlining the ways that market anarchy would solve the problems of providing the goods of law and its enforcement, and national defence. The final chapter surveys historical evidence to derive a set of conditions under which anarchic zones could be expected to emerge and thrive in a world initially dominated by states.
Previously I’d recommended The Machinery of Freedom (PDF, Paperback) by David Friedman and Chaos Theory by Robert Murphy as great texts that introduce the ideas of libertarianism/anarcho-capitalism. In my view The Problem of Political Authority is superior to either. It’s more comprehensive, easy to read, scholarly, humble and reasonable in its argumentation. I’ll be recommending this one until something even better comes along.