Student or Learner
"Evert Sunday he walks his dog around the city."
"Every Sunday he wanders his dog around the city."
"Every Sunday he runs his dog around the city."
The most common phrase is that someone walks their dog. If both the person and the dog are running, then you can say he runs his dog around the city. I have never heard of anyone "wandering their dog" and I would go so far as to say it's wrong. I would use "Every Sunday, he wanders around the city with his dog".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.