Hi, i have bought Titan Quest Anniversary Edition and i have installed it in my home PC.
I want to install it in my mother's computer also but i don't know if it's violating the agreement on GOG and the game.
I haven't do it yet.
Please help me

You can, there should t be any issue. Whilst technically you should only have one install for your own use, because the game is drm free you can install it when and where you like. Any reasonable use should be fine, and unlike the rest of the digital world you don't have to ask the owners permission each time.

Oh ma,isn't that cheating?

First things first, confirm from your mother that she really wants you to install that game on her computer.

Here is the answer from GOG's Support on Frequently asked questions.

Scroll down to Can I enjoy my purchases both on my laptop and desktop computer at home? question.

Being DRM-free means you can do whatever you want with it. It comes down to your own morals and conscience how far you take that.

If same household, definitely yes.

If different household, but you only play it (i.e. you play it, together with her or not, when you visit your mother) then also, definitely yes.

But if different household, and you want her to have second copy, then it's a no-no.

For a rule of thumb, consider it like a book. You bought it, it's in your house's library and anyone in your house can read it. Or if your mother lives away you can take your book with you when you visit her, and during your stay you can keep it in her library and you or her or both of you can read it. But you can't "duplicate" the book and just give her a copy to keep in her library. (rule of thumb of course; I know software works differently).