According to Wikipedia private equity is an asset class consisting of equity securities in operating companies not publicly traded on a stock exchange. A private equity investment can be generally made by a private equity firm, venture capital firm, or an angel investor.
There is another entity that can and has made private equity investments. That is Sovereign Wealth Funds or SWF's. SWF's are funds created usually by Central Banks from excess reserves. Usually SWF's are created by oil rich countries such as Norway or Saudi Arabia or export driven manufacturing companies such as China and Taiwan. Traditionally, SWF's would purchase safe assets such as US Treasury Bonds. However, with the growth of globalization have led to a growth in the amount of money in SWF's. So SWF's have diversified into other asset classes to try to get a higher return on investment.
Some common investment strategies according to Wikipedia are leveraged buy outs, venture capital, growth capital, distressed investments, and mezzanine capital. Those topics deserve a post of its own.