The Inheritance trilogy consists of Eragon, Eldest, Empire.
Read Eragon first, you will not understand Eldest, as it is filled with infomation and parts referring to the 1st book, Eragon.
Despite critics literally screaming "this is a weak copy of the LOTR trilogy!", these 2 (and hopefully 3) books are entertaining, absorbing, and serious fantasy. The unfortunate thing about these 2 books is that they do take a lot of influence from the LOTR trilogy. From the characters (Orcs) to the writing style (similar type of writing, and so on). But, as I said in my 'Eragon' review, no-one intentionally tries to copy, resemble, or poke fun at another book, unless the author is writing a parody.
Eragon seemed a little slow and dreamy at the beginning, but Eldest thrusts you into the action the moment you start. In Eldest, you follow the stories of two people, Eragon Shadeslayer, the slayer of Durza and rider of Saphira, and Roran Garrowsen, the uncle of Eragon. Eragon decides to travel to the land of the elves (ellesmera) to train his magic and swordsmanship. But along the way there is plenty of danger, magic, fights, sarcasm, and of course, adventure. Far away, Roran must defend Carvahall from Ra'Zac and orcs who invade almost everyday, trying to find, or even collect infomation about Eragon or Roran.
The one noticable difference between Eragon and Eldest is that Poalini's writing style has changed again. His writing has become noticeably more mature and darker, depicting scenes of evil more powerfully. In Eldest, Eragon is more like a man on a mission, rather than a teenager who is trying to find a certain area. There are less carefree moments for Eragon, and more 'I must follow my destiny' determination. This is by far a good thing for me, but for younger and less mature readers it might be a bad thing, considering that the pace of the book has dropped quite sharply. The Roran-Eragon switch every 40 something pages keeps you from concentrating on both characters.
Eldest is even longer than the already big Eragon (500 something pages, while Eldest is around 700 pages) I also find it increadible that Eldest retained the quality of Eragon, even though it is a sequel to a highly successful book. Though darker, more mature, longer, and slower-paced, Eldest still retains whatever qualities that Eragon has, while adding more details and information about Alagaesia. A fantastic book, even more so than Eragon.
If you have read Eragon, and not read Eldest, buy it and read it, if you have read none, buy both, and read.