The basic concepts behind antimatter is that every particle has a corresponding antiparticle, which has the same mass but opposite electric charge, along with the contrasting values from its other quantum properties, etc. When a particle and its corresponding antiparticle meet, they are destroyed in a burst of energy. This is often called "pair annihilation."
There are lots of risks involved when trying to contain 'antimatter' if stored in bulk. If you make a few screw-ups during the process, then you may as well crash into a giant flaming star or at least stick your head inside of a microwave for an hour; ha! We can effectively store positrons (positive electrons) and antiprotons, for example, and there is some use for antimatter in the medical field, as well. However, the question is more about if mankind can ultimately create high-speed antimatter spaceships without the help of extraterrestrials? Personally, I think most of the cool aliens use some type of crystal technology and zero point energy devices to power their crafts and flying saucers, but that is another subject entirely.
If you'd like to read a couple related articles about this subject, I found some decent resources online:
Image Credit: It is in the Public Domain because it was solely created by NASA.
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