IPO (initial public offerings): Where do the proceeds go?

When a company floats on the market and goes through an IPO, I would imagine the previous owner of the company would sell a percentage of his/her company to the market, and keep this money for themselves.

However in quite a few lectures I've had, the lecturer has said that an IPO is a source of finance for the company - would the owner put the money they made from the IPO back into the company (I doubt it), or are there examples (and it must be common) for companies to own themselves?

Your help is much appreciated on this subject, Google isn't helping me today!