In the introduction to the book, Friedman says the first two chapters are dedicated to the philosophy. Subsequent chapters are dedicated to how the philosophy plays out. Since I’m more interested in the philosophy, I’m not sure how much of the remaining chapters I will say anything about. But here are his thoughts on the role of government. This is from chapter 2.

2. The Role of Government in a Free Society

The classical liberal sees the appropriate means of arranging a just society as voluntary cooperation and free discussion. The market permits unanimity without conformity by being an effective means of proportional representation. Unanimity in this context means everyone can agree on the outcome.
Political channels, on the other hand, tend to require and enforce substantial conformity. An issue is decided by a yes or no vote, and the outcome must be applicable to all groups. In other words, in a marketplace, each can buy the version of goods he wants. We can get an overall sense of what the people want by watching what they buy, and even if a majority want one thing, other options are still available. But political issues tend to be one choice or another, with the one minority losing and the majority getting what they want.  

But there are areas where the market isn’t an option, or at least not a good one. For example: I can’t get one amount of national defense that I want, while you get another. We can debate over it and vote, but it’s going to be one amount for all citizens. Things like this are “indivisible items” that will require political channels to reconcile differences.

The use of these political channels tends to strain cohesion essential for a stable society, precisely because there can only be one answer, as opposed to allowing a marketplace to cater to varying needs. Fundamental differences in basic values aren’t resolved at the ballot box, they are merely decided.  

The widespread use of the market reduces the strain on social cohesion by rendering conformity unnecessary with respect to the activities it encompasses. The wider the range of activities covered by the market, the fewer the issues on which political decisions are required, and on which it is necessary to achieve agreement.  

Government as Rule-Maker and Umpire
Monopolies
Exchange is voluntary only when alternatives exist. Monopolies imply an absence of alternatives. Monopolies may arise because it is technically efficient to have a single producer- such as a telephone service. When technical conditions make monopoly the natural outcome of competitive market forces, there are three alternatives: private monopoly, public monopoly, or public regulation. All three are bad. These conditions can change over time though, and what once made monopoly the better course can be turned into a market.

Neighborhood Effects
Strictly voluntary exchange is impossible when the actions of individuals have effects on other individuals for which it is not feasible to charge or recompense them. The man who pollutes a stream is forcing others to exchange good water for bad. There may be a price at which they can be compensated, but they can’t, as individuals, avoid the exchange or enforce appropriate compensation.

Highways are another example. It would be extremely difficult for a private owner to build and operate a general access road with lots of entry and exit points. This is best done through taxes and the government.

Government on Paternalistic Grounds
Freedom is applicable to responsible individuals. But paternalism is inescapable for those that aren’t responsible, such as the insane, or children.