paleolithic period

The Old Stone Age or "Paleolithic" (paleo=old, lithic=stone) lasted from somewhere between 400,000 BCE to 7000 BCE.  People made stone tools, and survived primarily as hunter-gatherers.  Cooperation was critical in order to survive, so groups formed with kinship and pair-bonding cementing relationships.  These groups probably did not live in caves all the time like the cartoon image of the "cave-man", but were more likely nomadic, following prey animals and the seasons, perhaps returning to favorite sites seasonally. 
It is easy to think of the people of Paleolithic period as unsophisticated, but one theory about the way cave paintings were intended to be viewed reveals people "back then" to be much more like you and me than you might think.  The paintings often have what look like multiple versions of the same animal superimposed on each other.  Marc Axéma's and Forent Rivère have theorized this is because when the paintings are viewed via flickering firelight, it makes the images appear to be moving.  In a principle similar to that used in animation today.

video exploring cave paintings 
(by marc azema).

While It may seem like Paleolithic people were "living in harmony" with the natural world, and from the perspective of the 21st century, they were certainly extremely in touch with the seasons, and wilderness, they too had their faults.  There is evidence of war and fighting over prized hunting or gathering grounds.
A belief in some sort of afterlife is apparent in their burial practices and evidence for the development of communication, religious beliefs and a growing understanding of the plants and animals they relied on for survival are shown in the next great period of human history: The NEOLITHIC age.

neolithic period

The New Stone Age or "Neolithic" (new=new, lithic=stone) began somewhere around 7000 BCE.  Some groups made a shift to more sedentary settlement patterns and relied on agriculture and domesticated animals, while others continued to live as pastoralists, or quasi nomads,  bringing domesticated animals (cattle, sheep, goats, pigs etc.) along with them.
The staple crops which were first domesticated depended upon location, for example:
Mid East: Barley, Oats, Wheat and Legumes
West Africa: Yams, Millet and Sorghum
Americas: Squash, Corn, Potatoes, and Beans

humans invented a lot of things before they invented writing

Often people are judged by their ability to read and write.  But we should know better.  Like in the present day, just being illiterate, or coming from a culture which does have writing doesn't automatically make that person or their culture unintelligent.  People have invented a lot of useful and remarkably complex things without the ability to write down instructions for how to do so.
Some of the things invented in the Paleolithic and Neolithic periods:
Stone tools -which are harder to make than you might think
Marriage - pair bonding, although not necessarily heterosexual
Farming - planting certain seeds on purpose to increase yields
Animal Domestication - controlling which animals breed with which ones
War - unfortunately
Spinning and weaving - stone whorls and spindles and hand weaving of threads for clothing, fishing nets, and footwear from at least 21,000 BCE

The patterns of life and trade established by neolithic people are sometimes called "traditional economies"

The decision to settle down and farm a specific area came with trade offs.  The possibility for greater abundance of food and resources along with the certainty of knowing where that food was located were likely attractions to this way of life.  But good locations on which to settle permanently were relatively rare.  Most early civilizations focused around rivers for their abundance of water, fertile soil (in flood plains), and timber or other resources for building shelters.  
Once a group has a surplus of food, it would open up free time and energy for some people to work on other things,  The theory is that animal husbandry and agriculture led to still more efficient tools which allowed for still more crop production.  These things in turn led to other inventions  like writing (which historians are obsessed with because it seems to allow us to stop relying on archaeologists for information).  
But these greater resources and surpluses, combined with a comparatively fat and weak sedentary population meant these early civilizations were constantly vulnerable to attack by other groups who chose not to settle down.  
Hunting and gathering gets way easier if you are hunting for domesticated cows, and gathering from someone else's cornfield.
These proto-civilizations are celebrated among historians and economists as a kind of triumph for humankind.  They were supposedly organized on the basis of "tradition" where each generation learned from the previous one, and added to that knowledge.  Crafts and trades developed, leaders in the form of kings and priests emerged, and marketplaces for the trade of goods and services were formed.  We can see a bit of ourselves in this new way of life, people with specialized jobs, who live in cities.  But was this really the only way?
Nomads, and Hunter-Gatherers continued to exist, and one theory which highlights the miopic way Anglophone historians are biased in favor of farmers has been put forth by James C. Scott (in his book the Art of Not Being Governed)  to remind us that there is more than one way to organize a "civilization."
A video series that I often refer students to is the "Crash Course World History" by John Green on You Tube.  This episode on "Civilization" nicely elaborates on Scott's ideas: