What are diamagnets and paramagnets? A paragraph in my text reads:

An atom or ion with all electrons paired is not attracted by strong magnets and is termed 'diamagnetic'. In contrast, spins do not cancel when unpaired electrons are present. An atom or ion with unpaired electrons is attracted to strong magnets and is termed 'paramagnetic'.

That paragraph seems to state that diamagnetic things are, for most intents, non-magnetic things. Whereas, the following paragraph from the Wikipedia article on diamagnetism seems to state that diamagnetic things are, for all intents, magnetic things. 

Diamagnetic materials create an induced magnetic field in a direction opposite to an externally applied magnetic field, and are repelled by the applied magnetic field.

What are diamagnets? How do they relate to paramagnets?
 A: paramagnets = there are unpaired moments but the average of the-let's say-direction of the moments is pointing no where and we have zero net magnetic moment. but if we apply a magnetic field to this material, all the magnetic moments try to get in the direction of the applied magnetic field so the material a non zero magnetic moment.
diamagnets= there are no unpaired moments (atoms with completely filled atomic shells) and as you apply a magnetic field they do not want to change their stable state and according to the faraday's law there happens a n apposing moment to cancel the effect of the applied field.
now, i don't know if you were asking for something else or not?!
A: Both quotations you cite are correct.  All materials are diamagnetic, but diamagnetism is very weak and is easily masked by paramagnetism and ferromagnetism.
Any atom with paired electrons in its shells exhibits diamagmetism.  Paired electrons spin opposite to each other and cancel out their spin charges, leaving no magnetic domains in the material which can be aligned with an applied magnetic field.  Even though diamagnetic material can't become a magnet, it obeys Lenz's Law in the presence of an applied magnetic field.  Changes in the paired electrons' shells set up weak electric currents that induce a very weak magnetic field opposed to the field that caused the change.
Paramagnetic material is composed of atoms with unpaired electrons in their outer shell.  Unpaired electrons have a charge which makes it easier for an applied magnetic field to align them in the same direction.  While paramagnetism is also weak, and occurs in non-magnetic materials, the unpaired electrons create atomic magnetic dipoles which readily augment an applied magnetic field.  Thus, they act like magnets when they are in the presence of a magnetic field, which diamagnetic material does not do.
