After the adventures of Book 3, we go back in time a bit to see what Samwise and Frodo have been up to as they head east.
Three days since they took their leave to a mixed level of success. They're not altogether helpless in the wild, but they don't have the knowledge of the land and navigation that the older and more experienced members of the fellowship hold. The bleak is interspersed with snippets of humor, such as Sam and his rope.
The elven rope turns out to have some special properties - a slight glow in the dark and releasing itself from it's secure tie at the top of the cliff. Also that whole burning Gollum's skin thing.
Whatever Gollum once was, he's a far cry from the being once known as Smeagol, both in mind and body. I wonder how Frodo would have acted, had Gandalf not played such a strong mentor role in his life and this journey? What if Gandalf had not spoken of the importance of pity and mercy and Frodo instead just had Sam's (perfectly reasonable) suspicion and the call of the Ring?
Going to the movie, we're not going back to the beginning of The Two Towers, as Books 3 & 4 were interspersed together. Overall the opening matches up pretty well in tone and setting, but with a heavier emphasis on the Ring's (and Saron's) pull, but things diverge pretty quickly once Gollum enters the picture. Much of the dialog matches, but the action, setting, and timing doesn't. There's none of that trouble falling down the cliff, none of Sam jumping Gollum unaware, and no quick resolution in securing Gollum's obedience. Rather Gollum creeps up while he believes the hobbits are sleeping and makes a concerted effort to take back the ring, then the whole bother with the rope and Gollum agreeing to guide them happens the next day in full daylight.
This is really the first time we get to witness the genius of Andy Sirkus as Gollum, something that I eagerly look forward to more of. Looking at the vague memories I have of the film, I'm pretty sure that my strongest ones are of Gollum. I'm impressed how well the CGI has held up as well.