This question and variations on it are posted here regularly, and a search will give you quite a bit of reading. Here's an older one by maestro876 that's quite good.

As to "absolutely", most historians think Oswald did it. There is a photo of Oswald proudly holding a Carcano rifle. There was a series of receipts with Oswald's handwriting, showing he'd bought the rifle and the serial number. Oswald was seen bringing a wrapped, oblong object into the Depository where he worked, the day of the assassination. The Carcano rifle that had fired the bullets found in JFK was immediately discovered there in the building. It had Oswald's fingerprints on it and had the serial number of the one he had bought. In running away from the scene Oswald killed a policeman he encountered, like a desperate fugitive criminal not a bystander. How more absolute can it be?