||The main goal of this thesis is to acquaint with a mathematically correct analysis of the Ramsey-Cass-Koopmans model (RCK model). Firstly, this thesis investigates some basic results of the Solow model. The RCK model develops the original Solow model, therefore the results of the Solow model are necessary for the next analysis of the RCK model. Secondly, we will apply the calculus of variations to the optimization problem defined by the RCK model. Last but not least, we will study the dynamics of the economy of the RCK model with the help of qualitative analysis of systems of differential equations. Methods of this thesis are such a compromise between methods in current textbooks of macroeconomics and methods in original papers dealing with the RCK model. On the other hand, in this thesis there is an effort for sustaining of mathematical correctness of original papers.