Is it possible to understand (follow the story line) of Assassins Creed II, without having played Assassins Creed I?
Solution 1:
TL;DR: While you can start the series from the second game, I strongly advise to start from AC I.
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I've only played the "main" titles of the game (AC I, AC II, AC II brotherhood, AC II revelation and AC III), so what I'm about to write here is only true for the main series of the game (Released for Xbox, PS and PC) and might not be true for the games on the hand held platforms or Facebook.
Also, since AC II, Brotherhood and Revelations are all based around one main character I'll just call them all as AC II.
The AC series consists of 2 parallel story lines in each game, the story of Desmond, the main character, and the story of a particular ancestor. In AC I it's Altaïr Ibn-La'Ahad, in AC II, it's Ezio Auditore da Firenze and in AC III it's Connor. The story line of Desmond is continuing and enriches with every game, while the stories of the Ancestors are self contained and mostly do not continue into the other games, and since the ancestors didn't really know one about the other, if a previous ancestor is mentioned, there is a proper explanation about who he was and what is his importance to the story being told now.
Another thing is that just like many TV series, the game gives a "what happened in previous episodes" run-down in the start of each game.
So that when you start to play the game, no matter from what game you start, you will not feel left out of the plot, or that you have some hole in the plot. Especially if you've read the plot summaries, or watched the cut scenes.
HOWEVER, in my opinion, the games really do improve from one to next, especially from AC I to AC II, so if you'll start from AC II and then want to play AC I to replay the lost chapters, it'll be hard for you, as you'll be degrading you experience, instead of upgrading it. Not to say that AC I was a bad games, it wasn't and it's still a very good game, but the sequels are just much better.
An additional thing is the character of Desmond. While being the "real" main character Desmond, gets very little playing time, and stays very under developed in the games. By starting with Desmond in the first game, you are both pretty much in the same state of mind as you don't really know what is going on, and why are you in the situation that are in. I believe that discovering it gradually with him helps you connect to the character and care about him, while if you would start from the second game, where Desmond is already aware to most of what happens around him, and you are not really there will cause a disconnection between you and Desmond, which might make you not really care about the MAIN plot line of the game and the connection between the different episodes. For me the curiosity about what happens to Desmond was as much as an incentive to play the sequels as the wish to experience more of the Assassin's Creed fun game play.
Solution 2:
I would recommend skipping the first game entirely.
The trio of AC2 games (AC2/Brotherhood/Revelations) are completely understandable without having played the first game - the character you play in AC2/B/R (Ezio) has nothing to do with the main character of AC (Altair) until Revelations, and even then there's little correlation between the events of Altair's chapters in Revelations and the events of AC1.
You'll be a bit behind with regards to Desmond's story, but so little happens to Desmond in AC1 that it's not that big a deal. He spends almost the entire game in two rooms, and the plot development in the game occurs almost completely at the end, where it concludes with a cliffhanger. Desmond is also bland, and probably the most boring part of all of the games I've played to-date. At least in AC2, the people you can talk to outside of the Animus are mildly interesting.
Gameplay wise, AC2 evolves the formula significantly from the first game. While AC was good for its time, there are a lot of rough edges that get significant polish in the second entry and onward. It's a bit like the way Super Mario Bros. 3 is a significant evolution from the original SMB. As a new gamer to the series, you can get your assassination "fix" much better from the later games, and although the first game was a landmark in the series, it hasn't aged nearly as well.
The only issue I'd have with getting into the series now is that the AC2 trilogy is very similar - if you play them back-to-back, you'll probably be extremely worn down by the time you get to the end of Revelations.