Volume 3 of Law, Legislation, and Liberty is in part an attempt at identifying the reasons why, in Hayek's opinion, the principles of liberty he articulated in The Constitution of Liberty do not find greater subscription. Majoritarian democracy is not inherently just, since it is based on interests rather than justice. The majoritarian democratic system consists of people each pursuing their own interests: citizens want spending programs with others paying for them, elected officials generally want to be reelected, government workers prefer large over small government in order to enhance job security. The result is an aggregation of special interests, and not even the general, or common interest, let alone justice. The laws that end up being enacted are intended to serve specific administrative purposes rather than general principles.
With a system of progressive taxation, the aggregate tax burden is no longer felt by the entire population. People end up exerting political pressure for expenditures for which they believe others will pay. In such a system, any normal type of cost-benefit analysis of government programs disappears. The inevitable result is an ever-growing government sector.
The basis of the book is straight public choice theory (pp. 13-17 would make a splendid concise introduction to the field). Even a legislature elected by a democratic majority needs to have constitutional restrictions placed upon it, lest it become a form of tyranny. Hayek proposes "a model constitution" that attempts to rectify some of the shortcomings inherent in the existing democratic system. Laws should be general not specific. They should be about principles rather than benefits, i.e. they should protect citizens' life, safeguard their liberty, and help create an environment in which they are free to engage in the pursuit of happiness. Laws should not discriminate between different individuals or groups, not even based on their wealth or income. Laws passed must apply to everyone, including those who pass the laws, i.e. the legislature. This also goes for taxation: the burden of taxation is to be felt by all who benefit from the existence of government.
Law, Legislation, and Liberty was intended as a sequel to The Constitution of Liberty, in that Hayek wrote it to "fill in the gaps" that he felt existed in his argument in that earlier work. He wrote and published Law, Legislation, and Liberty on and off over a time-span of approximately 15 years (early-mid 1960 to mid-late 1970s), which were in part interrupted by ill health. Hayek admits that the result is at times repetitive and lacking in organization. The reason why he did not go through the effort of redoing the entire work upon completion is because he thought he might at that rate never finish it (he was 80 years old by the time volume 3 was published).
There are still plenty of great insights, which Hayek argues persuasively and in doing so manages to portray as common sense. There are also plenty of flashes of that true rhetorical brilliance characteristic of Hayek that can make his writings such a feast to the ear and mind. On the downside, however, these rhetorical gems are hidden in a large volume of pages that at times do indeed seem tedious, repetitive, and unorganized, unlike with The Constitution of Liberty, where they literally seem to jump off the page at you. All in all, read The Constitution of Liberty first, as Hayek himself suggests. And if you're not up for reading the approximately 500 pages that make up the complete Law, Legislation, and Liberty, two chapters (30 pages total) in the book The Essence of Hayek make for a comprehensive summary exposition of the ideas in the entire trilogy ("Principles of a Liberal Social Order", ch. 20 in The Essence of Hayek, covers vols. 1-2, and "Whither Democracy?", ch. 19, covers vol. 3).