Judaism has an afterlife of sorts, other than Heaven, in Gehinnon, as described in more detail in this answer.1 Gehinnon is not like the Christian Hell, however.
While some get no afterlife at all (see note below), for most, Gehinnon is a temporary residence, while the departed is under divine judgement. The departed stays there for no more than one year before moving on to Heaven, which is why our custom is to say Kaddish Yatom, the mourners' prayer, for a maximum of only eleven months -- lest we give the impression that the person was so wicked as to require the full twelve months. I don't know a lot about Christian afterlife ideas, but our Gehinnon is probably closer to your Purgatory.
Judaism doesn't condemn souls to eternal damnation and torment. Judaism recognizes that teshuva, repentance, is possible and that divine punishment is not permanent. No external force is required to "save" a soul; we are each responsible for our own salvation, by clinging to God and doing as He commands. If we messed up in life (as we all do), we can still recover. (So what's Kaddish Yatom about? It's more about asking for leniency than "saving" the person. Only God saves us.)
The Messiah, on the other hand, redeems us on Earth, by gathering the exiles, building the Temple, bringing peace, and more. Sometime after the coming of the Messiah we reach the end times, which includes resurrection of the dead, but that's all done by God, not by a mere human.
1 Your question was about Hell, not the afterlife in general, but I'll add here what DonielF said in a comment:
The relevant passage by Maimonides regarding the afterlife for Jews is in Mishnah Torah, Hil. Teshuvah 3 and 8, and regarding the afterlife for non-Jews is in Hil. Melachim 8:11. To summarize the more pertinent points, the afterlife is not one size fits all. For Jews, one who sins goes to Gehinnom for some amount of time and then goes to Heaven, but it depends on his good deeds in this world what level of Heaven he gets. However, one who does one of 24 specific sins loses his entire afterlife and ceases to exist upon his death. Non-Jews can earn their share by fulfilling just 7 mitzvos.