That's a very broad question that can mean different things to different people. Answering it and understanding each other is hard due to the semantic complexity. It also contains an emotional dimension that cannot be described analytically.
Here's my take: Yes I do believe that everyone has a soul and it comes in two intertwined flavors; the nonlocal and the local soul.
The local soul is local in space and time. It's what makes you unique. For example your beliefs, thoughts, actions and so on.
The nonlocal soul isn't localized in space or time, but rather exists on a fundament level just like say quantum fields seem to do.
Within all of us exists a dynamic between the two, from rejection to enlightenment. One isn't better than the other, it is simply a duality that exists and that is meaningful to all of us in some way.
I also believe that time and space are an illusion. Our perception is supervenient on entropy. For example when someone dies they seem to be gone, but they are actually still alive in the past. And so this unifies the local with the non local.
Looking forward to replies.