Since the begining of child's arrival in the world, it begins to explore its surroundings, discovering in various ways what possibility and ability it has. Child's cognitive development can be affected by parents, social and emotional environment, and playgames. These factors can allow normal growth and development for the child which allows them to experiment with different materials. The cognitive development encourages children their development of self - concept and they learn about terms such as size, shapes and colours. In order for child's wealthy growth, it is necessary to provide him a safe, warm and stimulating environment. The main goal of this work was to process the overall cognitive development of a child, from its birth until it is ready for school, and it implies sensomotor development, thought development, conclusion and a child's method of problem solving. By learning, the new brain stimulations are being created, and these stimulations become information that enables us to solve problems and to understand the environment we live in. In this work, I have also introduced theories of cgonitive development by well - known psychologists Jean Piaget and Lav Vigotski, in which are elaborated child's development by its chronological age.