He was on his way to his extra classes when he happened to see the old man just staring through a window right at him. He walked over and opened the window to see what he wanted, but right when he did the man just disappeared. He decided to ignore it for now and just go to his classes. He made his way there and learned about what all the slayers actually do. He learned that they actually go around the world to lessen the amount of monsters out so people can move about the world without getting attacked.
He went to his next class and learned about the safety procedures to keep himself and everyone else safe while slaying monsters. He found out that when slaying monsters he has to be able to clear everyone out of the area before he tries to slay the monster. If you don't get everyone out of the area, it poses a risk to their lives. And once you slay the monster you must dispose of the body either by burning it, or calling the clean up crew to deal with it.
He decided to go back into town to find the mysterious old man that keeps popping up. He made his way to the main road where almost everyone hangs around. He looked around the area but saw no sign of him. He asked the locals if they'd seen him at all but had no luck. He decided to just give up and to just go home and rest. Once he got home and sat on his couch to watch a show, he saw the old man outside his window. He ran out the door to confront the man, but when he got there the man had disappeared again.
He decided to ignore it again and just go rest till morning. In the morning he went back to school to fight some more training monsters. He went to the next class after that and learned a few more techniques that could help him defeat even tougher monsters. After that he went back to town to see if he could find the old man. He went around asking people again if they'd seen him. He was having no luck till he saw him over on a bench in the park.