It is a very good book, easy to understand, the normal mathematic basics are all you need to understand the theory of this book.
He begins with the Solow growth model. It is a static model and can't explain growth over time and the differences between countries in output per person. From that point of view he turns to the Ramsey model. The overlapping generation model is a special case of the Ramsey model. Diamond developed a good model for dynamic analyses. He uses the overlapping generation model for wealth aspects. All models can't describe growth within the economy. It has no productive factor produced in a growth model, like the ak-model. The endogenous growth model deals with it and discuses growth from different point of views. He concentrates on a special model of knowledge. Human capital is introduced later in the Solow model. Knowledge is symbolized in the R&D sector. The Romer model is based on it. The company sells the knowledge via a patent to the market and the rest of the economy behaves competitive. Finally the endogenous growth model is tested. The difference between countries in their output per person comes next. He uses the Solow growth model with human capital. Most of the differences come from other factors. Social infrastructure is a way out and introduces several aspects especially lobbying, tax benefit, rent seeking and geographical factors. The real business cycle based on the Ramsey model. The fluctuations are modeled from the balanced growth path. Two disturbances are modeled, technology and government purchases. Money has no influence in the real business cycle model. It is modeled in the rigidity chapter. Here you have the new Keynesian model with modern fluctuations and rigidities on prices wages and incomplete competition. The IS shock is introduced and how money influences the prices and output. It includes the Phillips curve, menu costs and the Lucas model. The static rigidity model is combined with the real business cycle model. The dynamic stochastic equilibrium model tries to form a time dependent model. It is a Walrasian model with effect of monetary shocks and shows the influence of rigidities to prices and output. In this model the prices are fixed before or during different periods. The result is a modified Phillips curve, the new Keynesian model and a microeconomic based foundation.
Consumption and Investments are the inputs in the growth model and they are very important to fluctuations. The consumption chapter is based on the permanent income hypothesis. The investment chapter is based on Tobin's q and it is stressed against interest fluctuations and tax policy. The financial contract is characterized by asymmetric information. The investor and financier are presented by an equation and the optimal solution is represented.
The labor market is a non Walrasian market, like it is explained in the real business cycle model. The departure from the equilibrium is described with the
efficiency wage. The labor market is a heterogeneous market and there are searching and matching problems. The contract model explains the rigidities of wage contracts.
The last two chapters are a bout macroeconomic policy. The monetary policy is about the right measure to fix the inflation rate to a low level and find an optimal policy for setting the inflation target. The last chapter includes the government in the growth model and debt models are described.