As children grow and develop, so does the way they play. American Sociologist and Researcher, Mildred Parten Newhall (1902-1970) identified six stages of socialization children go through as their play progresses.

Parten's Stages of Play
1. Unoccupied Play
This is the initial form of play for babies and young children. There's no clear purpose just lots of random adorable movements from little ones as they discover how their body moves and learn about the world around them.

2. Solitary Play
It's all about kiddo at this point. At this stage little ones prefer their own company and play alone. They are very happy to entertain themselves and may tune out everything else.
3. Onlooker Play
At this stage children start checking out how others play without actually joining in. They start picking up new skills by actively watching and listening,

4. Parallel Play
When little ones play around each other without actually interacting, they are . This is also the stage where they start learning concepts like what's theirs and what's not.
5. Associative Play
This is the stage where children start playing and socializing with others but they're not coordinating or organizing their fun yet. At this stage they start learning about sharing and cooperation and continue working on their language and problem solving skills.
6. Cooperative Play
At this stage kiddos are very much into socializing! They care about others and what they are doing. As children interact they begin to learn social rules like how to share toys and ideas, follow rules, and develop a sense of what's right and wrong. Play at this stage is coordinated and organized. Activities may have roles assigned and a group identity may emerge.
References:
How kids learn to play: 6 stages of play development. (n.d.). pathways.org/blog/kids-learn-play-6-stages-play-development
Rebecca Staples; Cochran, Moncrieff (2008). "Parten, Mildred (1902–)". Early Childhood Education: An International Encyclopedia. Volume 3: O–Z. Greenwood. pp. 592–593.
Bernard, J. (1970). Mildred Parten Newhall 1902-1970. The American Sociologist, 5(4), 383–383. http://www.jstor.org