http://www.esa.int/esaSC/SEMM17XJD1E_index_0.html

the most interesting thing about the Lagrangian points is that the technology exists today, or rather the technology behind the points are a natural phenomena. It involves the gravitational pull between different large cosmic bodies (planets, moons, stars, and so on) to keep a object of insignificant mass by comparison , in a stationary position. This means with the rite calculations to maneuver satellite , or other man made structure into these points could theoretically keep them in place with little or no adjustment needed to keep it's location. With much less power needed to keep it in space, longer term observations, experiments, or possibly even habitation would be possible without having to deal with the troubling task of transporting new resources to keep it in space.

http://www-formal.stanford.edu/jmc/whatisai/whatisai.html

artificial intelligence is a man made computer intelligence. Although the meaning is broad and has changed slightly over the years, typically what most think when they hear about AI is sentient computers. The study of AI and how to properly achieve it has been on the mind of scientists for decades, and although there has been some progress, intelligence of the human level or above is still far off from the looks of things. The possible uses for such a technology are hard to list because there are just about as many uses for it, as there are for humans in general.

http://www.understandingnano.com/index.html

nanotechnology involves manipulating/creating things on an atomic and molecular scale. In a nutshell it's the science of creating anything by piecing it together with the most basic building blocks available (not going into advanced theories involving even smaller units). The use of this technology is just as vast as AI, with the ability to create microscopic machines, or even organic machines, you could do a variety of tasks. An interesting application would be engineering a biological machine that could be programmed to assist the immune system against a certain virus, or possibly even be used as a way to remove cancer cells from normal tissue and then assimilate itself into the removed area as a replacement for what the cancer cells use to be. Besides the benefit to the medical field, nanotechnology could be used to create extremely strong materials, since the technology involves working on such a small scale, the ability to accurately engineer stronger materials should be much easier, and produce far greater results than conventional methods.