A simple Phillips curve can be written as gw=-e(u-u*), where gw is the wage inflation rate and gw=(Wt+ 1-Wt)/Wt, where E reflects the sensitivity of nominal wage growth rate to the change of unemployment rate. By taking the derivative of u, we can see that gw and u change in opposite directions. Therefore, there is an alternative relationship between inflation and unemployment, that is, there is a short-term trade-off between unemployment and inflation. Based on this, the government can formulate macroeconomic policies and choose different combinations of unemployment rate and inflation rate.
Revised Phillips curve, Friedman and Phelps, and put forward additional expected Phillips curve. The Phillips curve with additional expectations can be written as p=p*-e(u-u*) and p=gw, which means that unemployment depends not on the level of inflation, but on excessive inflation that exceeds the expected inflation.
The long-term Phillips curve is vertical, which reflects the idea of currency neutrality, that is, in the long run, government policies cannot reduce the unemployment rate by raising the inflation rate.
Stagflation mainly comes from unfavorable supply shocks.
In this regard, we can refer to some macroeconomics textbooks, such as Man Kun's Principles of Economics, which is relatively basic, and Dornbush's Macroeconomics, which is intermediate. Neither of them is very difficult.