If you’re curious to read the original comic book adventures of Jessica Jones, possibly coming soon to a TV screen near you, most of her comic book stories are available in trade paperback form.
Sadly, the original Alias Omnibus hardcover collecting her entire original series is out of print and very expensive, so your best bet would be to check out issues of her original series as softcover paperbacks. Be aware these comics are not for kids. Jessica the comic book character has quite a potty mouth, and she does some things you don’t really read about too often in comic book form. Those issues are available here:
Alias: Ultimate Collection, Book 1 (reprints Alias #1-15
Alias: Ultimate Collection, Book 2 (reprints Alias #16-28
If AKA Jessica Jones becomes a TV series, it’s a safe bet to assume that these issues will be reprinted again as many Alias collections are going out of print.
Jessica Jones’ comic book adventures continued in the more suitable for all ages comic The Pulse. This series had stronger ties to the Marvel Universe, and didn’t always focus on Jessica. Here are those collections:
The Pulse Vol. 1: Thin Air
The Pulse Vol. 2: Secret War
The Pulse Vol. 3: Thin Air