Geez, this is kind of a tough question. Most people are familiar with the four basic states of matter that occur on earth: solid, liquid, gas, and plasma. Plasma is kind of a debated state: it is an ionized gas, so some people want to classify it as a gas. In similarity, there is supercritical fluid, which has the density of a liquid but the properties of a gas with respect to boiling points. People also talk about a gel, which is a plastic state of matter; this is like a solid but it completely takes the shape of its container like a liquid but its not a liquid. It's hard to talk about because if you use the terminology (like solid, liquid, etc) to describe something that is not actually one of these states, you are basically contradicting your description.

This all comes from the ability to compress, expand, heat, and cool things at levels never before thought possible, usually requiring insane amounts of energy. The Bose-Einstein condensate I think is when a gas is cooled to absolute 0 (-273 C, or about -459 F) and the sigma and pi bonds that were holding the atoms together turn into strings and make a kind of liquidy-substance. To get to temperatures this cold, you have to have a chain of pressure cooling chambers and various kinds of gases, and again, lots of energy. There are more forms of matter found in space, which have been replicated in labs; I don't really know much about these, only the solid, liquid, gas, plasma, supercriticals, etc.

Remind me in 2 semesters and I'll tell you much, much more!