Keynes (in a nutshell) is a state-economist, and believed that the state can act as facilitator of the economy, rather than impedement (I think he is wrong). As such, the State should follow simple guides, especially regarding taxation and spending (fiscal policy). Basically, save in the good times, to spend the extra in the bad times, and use those spending on public works, or the like, to stimulate the economy. Keynes ideas help promote "the middle way," "the New Deal," and the soviet and Chinese numerous "Five Year Plans."
Keynes is the primary model statist economist and politicians "use" (not becuase they know anything of economics or keynes, but, ebcause they are the government). However, it's hugely corrupted a way diverted away from Keynes intentions even. Government has further corrupted a corrupt economic philosophy. States typically SPEND in the good times, and BORROW and SPEND in the bad times.
Milton Friedman, is know as a monitarist, of the Chicago School of Economics. Very free trade, but they tend to focus on money and money supply issues, and the ways they can assist or injure an economy. Federal Reserve Rates, Fractional Reserve Banking, inflationary policy and problems tend to be their focus. Friedman is often considered a supply sider, though I don't think it's accurate, and definately not a Reagan-Supply-Sider. He's also very critical of the state's ability to actually manage an economy, becuase of the "lag effect." By the time state planners get the information on the economy and interpret the information, economic situations and circumstances have changed. As they then plan, and yet implement that plan, the economy has changed yet again, and the application of the plan is often inappropriate for the new situation, and causes harm.
F.A. Hayek, and his mentor Ludwig Von Mises are of the "Austrian School." In my opinion, these are the TRUEST writings of economics. They explain and study what economy, trade, money,
prices, interest, savings, and the like are really about, the benefits and their problems. They also explain economics devoid of any state apology, and often note and recognize the adverse effect states and state planning have on economies. They are very very free-traders, and lay the foundation of understanding necessary for anarcho-capitalist economic systems. They also solved the classical problem of the water/diamond paradox, through use and promotion of the
subject theory of value.
It is my recomendation, that one visits
www.mises.org for the best study of economy. NUMEROUS texts and lessons are available online and free. If you're feeling courageous, Human Action by Mises, is the best (and quite difficult, only because he's Austrian, and wrote like an Austrian) economics text I have read so far.
Not to mention, Mises, Hayek, Rothbard and Sowell offer many historic and current criticisms of Marx, Keynes, Soviet or Chinese economic systems, and a host of current American and international policy issues by a range of other contributing authors.