Can a cisco wifi adapter AE3000 extend my wireless range? I want to connect to some hotspots about 1/2 mile away from me
If you're using a crummy old wireless-B PCI card from ten years ago, yes, you may experience an increase in range when plugging in a Cisco AE3000. If you're using a wireless-B router to go with it, no.
Regardless, you won't get a half mile range. To accomplish this you will need an antenna with a narrow field that results in very high gain within that field, and you will need to aim it at the source, preferably a source with a similar antenna. Look in to 802.11AC and maybe a cantenna.