I heard, that AD&D is a BIG manual, where written all about creating an RPG. But from other sources, I knew, that it is a game. What exactly is it and, if it is a manual, could I download it?

It's a huge manual with all the little rules and references necessary to play a pen & paper RPG.

however, many PC RPGs are based on its ruleset, particualrly the BlackIsle ones like Baldur's Gate, and most owe more than a little to D&D. There was a terrible cartoon based on it, too.

I play Dungeons and Dragons all the time. It is a pen & paper game where you make characters, go on quests, and interact with the fantasy world. One person is the Dungeon Master, and he controls everything that the players themselves cannot. ALL modern RPG's have some base in Dungeons and Dragons. There are three 250 page books, the Players Handbook, the Monster Manual, and the Dungeon Master's Guide. They can be bought from The Dungeons and Dragons website. If you find a place to download them for free, IT IS ILLEGAL. The newest edition of rules is 3.5, but just plain 3 works too.

AD&D is a pen-and-paper RPG. You can buy a starters kit with the players handbook, but you really have to buy it. (sorry if I'm repeating what the others said...)

Player's Handbook is enough for the start, and I'm not sure but I think that AD&D 2nd edition products are free to download, I'm not sure, but it's still better if you have a book in your hand...

NO Nothing D&D is free to download except missions.

IMO the D&D game got downwards since it was bought by WoTC, I'm still sticking to 2nd edition, although I actually played the 3rd one before, the only thing better is calculating AC and To Hit, but that can be easily converted into 2nd edition...

2nd edition is lacking in many of the areas that were improved in 3rd. THACO was very confusing until you got the hang of it, and the whole saves thing was simplified.

You can easily calculate THAC0 and AC as in 3rd edition, you just turn around the numbers a bit and - that's it, but what I don't like in 3rd editon is the skills...
I mean let's say bluff, that's something you roleplay in 2nd edition, but in 3rd you just roll a dice, the same is with skills like Gather information or diplomacy...
Another thing I don't like is too fast character advancement it's to easy to achieve a high level...
The 3rd edition is too much Hack n' slash oriented, but in the end it all depends on the DM...