The actual beginning of theatre is hard to track since it seems started with the establishment of society. The literal meaning of the word theatre is a pace usually buildings to see a dramatic performance. In fact, theatre means lots more than a building. It brings a group of people into one or a series of stories and bonds their emotion together through the special format of performing arts.
Ancient Greece is thought to be the root of theatre since the first written record for theatre in 600 B.C. However, this is probably a narrow way of talking a theatre. If you look it in a broader way, take tribal dance and religious rituals into account, it can be dated back to at least 8500 B.C.
Theatre, depending on how you define it, goes hand in hand with society as it has always been a part of life to express and perform in some way or other.