Classical Keynesian Monetarist
Labor demand and labor supply are brought into equilibrium by the real wage.  As a result there is no involuntary unemployment. Workers and firms bargain for a money wage, not for a real wage.  Money wages adjust slowly and workers resist any drop in the money wage. While not putting forward his own theory of the labor market, Friedman argues that people do tend to think in "real" terms and not in nominal amounts.
Saving and Investment are brought into equilibrium by the interest rate.

Investment responds to the interest rate.

The interest rate is simply set by the interaction between saving and investment, in a loanable funds market.

Money demand is simply a transactions demand.  In general, money has no effect on the real economy.  Raising the money supply simply pushes up prices.

Saving and investment are brought into equilibrium by changes in income.

Investment is unstable because it is strongly influenced by expectations of the future, which is uncertain.

The interest rate is set by movements in and out of financial assets -- by decisions of wealth-holders of what form to hold their wealth in.  It is thus unstable.

Money demand is affected by transactions, but also by other things, in particular fear, which may lead to a "speculative demand" for high money balances.

Money demand is mainly a transactions demand -- a stable function of income.  There are other assets besides money and bonds that people can hold, including some consumer goods, so speculative demand for money is unimportant.

A consequence of this is that any increase in the money supply spills over directly into increased purchases (consumption), which it will not do in Keynes' system in which consumption depends only on income.

Hence we get Classical result that inflation is caused by too much money.

Stable at full employment. May be stable at many different levels, including levels with substantial unemployment.  Givernment spending may raise output.  In the long run, tends toward full employment.  May diverge in the short run, but (a) this is short-lived and (b) divergence is likely to be the fault of government.
Way of
Quantities adjust smoothly and rapidy to prices.  This can be seen above in the adjustment of the labor market to the wage and the loanable funds market to the interest rate.  A modern economy in which production takes time, large capital expenditures are made on the flimsiest of guesses about the future, and in which the financial system permits rapid trading of financial assets, works differently from the economy envisioned by the Classicals.  In this world quantities adjust to other quantities. Strong faith in the ability of the private sector to produce growth and stability if it is not constrained by government. 
Laissez-faire: No government role. Keynes argued that a government role was needed to preserve capitalism because without management, a modern capitalist economy is so unstable that it may threaten the social compact that it rests on. (See Dillard -- people's willingness to tolerate large disparities in wealth.) Friedman is a libertarian, opposed to government interference on principle.  He is both more optimistic than Keynes about the inherent stability of capitalism, and much more suspicious of the state.  He argues that government, even if well-intentioned, bungles intervention.
Heyday Late 1700s to 1920s 1930s-1960s (Depression plus apparent success of government intervention) Late 1970s-Early 1980s (High inflation)