The Predation reference article from the English Wikipedia on 24-Jul-2004
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Predation is an interaction between organisms (animals) in which one organism captures and feeds upon another called the prey. The predator is usually the larger and stronger of the two. Predators are always either carnivores or omnivores. The prey might typically be a herbivore, but some predators feed on anything they can capture, including other predators.
Predation by a centipede on a large spider
This centipede crawled up under the eave of a shed to capture
and feed upon a predatory cane spider hunting there (enlarge)

Humans naturally think of large cats (lions, tigers) and large reptiles (crocodiles) as typical predators, or perhaps even snakes, many of which are predatory on small mammals. However, spiders, centipedes, most lizards and turtles, and frogs are also voracious predators.

Contrary to popular belief by some, predation is not typically a indiscriminate urge to kill other living beings. When hunger is not an issue for the animal, most predators will typically not seek to attack prey since the basic need is absent and it is a waste of energy to do so in that situation. For instance, a large predator fish like a shark that is well fed in an aquarium will typically ignore the smaller fish swimming around it while the prey fish take advantage of the fact that the big fish is apparently harmless and treat it as simply a big but equal inhabitant of their living space.

In addition, it has been observed that well fed predator animals in a lax captivity like as a pet or on a farm will usually differentiate individual prey animals who are familiar coinhabitants in the same human area as opposed to wild ones outside the area. This interaction can range from simply peaceful coexistant to close companionship. In contrast, the predator animal typically treats prey animals from outside the human's influence as fair game. This can be because of either cultivated affection for those individual animals and/or the humans have made clear to the predator that harming these particular animals will not be tolerated. A good example of this is that there are numerous instances of pet cats and pet mice living together in the same human residence without incident as companions.

In addition,

The Volterra-Lotka equations describe a simple mathematical model of the interaction between predators and prey.