I’ve written a little bit on this page about the East Semitic languages of Akkadian, Babylonian and Assyrian. There are some wonderful books out there to start learning for around $20 or $30, notably Marcus and Caplice (and Worthington, if the grammar is your interest). But you might want to start for free. In which case, I recommend the Akkadian Lessons at Knowledge and Power’s Cuneiform Revealed website. The lessons are short and simple, and there are sample texts to work through on your own as you work through the lessons. Two warnings: The free lessons require you to work through them with less hand-holding than you get from Caplice. And they are in an older font, not the carefully worked version of Neo-Assyrian that predominates in academic publishing. (You will need to download the display font; instructions are at the website.) That said, transitioning between Babylonian and Assyrian fonts is not as difficult as some make it out to be and this is a great way to be able to say that you read a bit of Hammurabi’s Code without an excess of effort or a large investment.