Piaget
According to Jean Piaget's theory of development there are four stages of cognitive development. The first stage is the Sensorimotor Stage, which starts at birth and extends until the infant is about 2 years of age. During this stage infants gain knowledge through actions that allow them to directly experience and manipulate objects around them. They also gain practical knowledge about the effects of their actions, such as grasping or pushing objects. A major mile stone in this stage is object permanence, which occurs at the end of the stage, where the infant realizes that just because they can't see an object it does not mean that it does not exist.
The second stage is called the "Preoperational Stage" and appears between birth and two years old. In this stage children are just beginning to develop their thinking skills and can use words, symbols and images to represent the world.
The third stage starts at about the age of 7. This is called the Concrete Operational Stage. This is where the child becomes logical, but is only tied to concrete activities and tasks, meaning they can produce relationships and think in a sequence.
Then when the child enters adolescence, they move on to the final stage, called the "Formal Operational Stage". This is where the child can think abstractly—understanding algebra, for example.
Read more about this topic: Infant Cognitive Development