It's hard to get an exact answer, because there isn't always accurate information about when a company started trading. For instance, many companies that later became famous were small family businesses for a long time beforehand. However, if you type 'worlds oldest company still trading' or similar into a search engine, you will find several lists.

One of the most interesting, listing several European companies going back to the 17th or even 16th centuries, is here.

One of the oldest companies is Lloyds of London. It began as a coffee house in the 17th century, and by 1688 was well known as an insurance trader, which is still its main business today. Despite a number of scandals, especially in the 1990s, the company is still going strong.

If you stick to one country you can find much older businesses, but many of these are very small. This list, for example, is just for Britain and has one small business apparently founded in the 12th century.