This is a common question from students admitted to law school, but it also comes up among those thinking about law school--I get both often from blog readers, so perhaps this post will help some of those readers.
Most of the published advice I have seen about what to read before law school is awful. Repeatedly, I have seen law professors recommend the American legal realist classic The Bramble Bush by Karl Llewellyn from 1930. I am the Karl N. Llewellyn Professor of Jurisprudence here at Chicago, and there is no doubt Llewellyn was a brilliant lawyer and an iconoclastic thinker of central importance to American law in the 20th-century. But The Bramble Bush is unintelligible to anyone who has not already studied law and read many judicial opinions. I teach parts of it every year in my basic Jurisprudence course, which is open to first-year students, but only after two terms of legal study. Any novice is wasting their time reading it.
Another favorite, but misguided, recommendation is Edward Levi's classic An Introduction to Legal Reasoning. Levi spent his career here at the University of Chicago, and was Dean of the Law School and also President of the University, as well as Attorney General of the United States under President Ford (this was before the Republican Party became FOXified, such that no serious person, like Levi, would go near it). Levi's book is also a tour de force through common law reasoning, but it is not for beginners. It should not have been called "an introduction" rather than "Legal Reasoning in Reality."
But there are two books that can actually be read by smart students before law school and will help them understand what is going on during the first year.
The first is Frederick Schauer's Thinking Like a Lawyer. Schauer's book is, in essence, Levi's book but actually written as an introduction. Schauer is a major figure in contemporary jurisprudence and constitutional law, but he here brings to bear plain language and simple explanations about law and legal reasoning, discussing rules, precedent, reasoning by analogy, statutory interpretation, and other topics.
The second is Ward Farnsworth's The Legal Analyst. (Farnsworth is now the Dean of the University of Texas School of Law, but came to UT well after my time.) Farnsworth, again in lucid and intelligible prose, introduces a variety of legal problems--drawn from tort and contract law in particular--and shows how a variety of analytical tools, especially (but not only) ones derived from baby economics, can help understand them. (By "baby economics," I mean the claims that follow from the assumption that people in capitalist socieities are instrumentally rational in trying to get what they want, and that law acts as simply another incentive affecting that instrumental reasoning. The tools and categories of baby economics are now omnipresent in American legal education, since Richard Posner's attack on conventional doctrinal scholarship in the 1970s.)