||In this work I summarize mathematically rigorously knowledge about market equilibrium. The work has two main parts. In the first part I am dealing with existence of the market equilibrium. It means to find a price system that satisfies conditions of the equilibrium. Firstly all needed terms are defined (commodity, producer, consumer, economy, equilibrium etc.). And secondly Kakutani's theorem is introduced and its application in the proof of equilibrium existence is explained. Mathematical assumptions and their economic interpretations are discussed in detail. In the second part is the equilibrium stability problem analyzed. With usage of the theory of differential equations the nature of equilibrium is investigated. This means if the price system is going to the equilibrium. There are demonstrated few approaches in the work that employ the stability of so called linearized system or the method of Liapunov functions.