jremington:
Most laptop batteries are LiPo and need to be charged and discharged properly, or they can be destroyed in the very first use.I have obtained good quality batteries at reasonable prices from http://www.all-battery.com/
Most laptop batteries are not LiPo, they are lithium ion, not lithum ion polymer, which is
much more dangerous (for instance must never be charged unattended).
The normal recommended regime for laptop batteries that I've heard of is to fully charge
and discharge them about 8 times when new, then occasionally subject to a full discharge/recharge to maintain capacity. And yes all lithium batteries must always
be charged and discharged under proper battery management (which will be the case in a
phone or laptop).