Hi,
I recently took courses in using Adobe Photoshop, Corel Draw and Adobe InDesign and I'd like to start working on my stuff but since I'm still kinda unemployed I'd rather stick to some open source alternatives. So do you know any free but powerful enough alternatives to the above mentioned software? And do you know any good tutorials and tips for them?
I know I could google up something, but I'd rather get the opinion of someone who actually knows something about it or uses it.
I'd really appreciate any good advice on this.

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I use paint.net if I'm doing some light graphics works. I find it far more intuitive than something like GIMP to use, and I heart the "import to layer" function. It makes combining elements from backgrounds, cutouts, text snippets, etc, way easier to integrate into a single piece, in MY opinion.

There's a 64 bit beta version that I recommend if you have Windows 8/8.1.

I did this in just a couple minutes with paint.net

Let's start with Inkscape perhaps?
Perhaps Scribus for page layout?

Some people speak highly of Krita.

Depends on what you want, really. The big three are:

GIMP, the Photoshop wanna-be. People say it's hard to use but I never got that. Weird, surely, but difficult? Eh.
Inkscape does vector graphics and does that well. Some people argue you can vector in GIMP too, but Inkscape's better for it.
Krita is oriented towards painting with a hardware drawing tablet, and good for that. If you don't have a tablet, or don't want to do digital painting type of work, GIMP is better.

As with most things open-source, there are lots of other contenders out there, mostly unfinished or not very good. I have a soft spot for GrafX2, but that's an oldschool/Deluxe Paint-ish tool so probably not what you're looking for.

Definitely have a look at Krita, ive used it (not professionally) and like it. Its been getting a lot of heavly development and its a pretty strong package. krita.org

(its part of the calligra suite (office suite))

The other usuals are gimp, and inkscape which are good as well.

The most well-known ones have already been mentioned, here's my take on them:

GIMP for raster graphics, on just about any platform under the sun.
Quite different to what you're likely used to, but very powerful. I do miss a few features from Photoshop CS5 (smart objects, primarily, but also 3D), and am still getting used to the behavioural differences.

Paint.NET for raster graphics, Windows-only.
A much more light-weight than Photoshop or GIMP. Several years ago, I used Photoshop for heavy lifting and Paint Shop Pro 7 when I wanted to to a quick touch-up or test, and speed was more important than pixel perfection (say, for pasting a screenshot and adding a couple highlights), Paint.NET took over the latter's role (I absolutely detested later versions of PSP, and moving away from pirated software is only good - I bought the Creative Suite 5 package though, because I got it cheap as a student).

Inkscape for vector graphics, multiplatform.
Not as different from Illustrator as GIMP is from Photoshop, but still different enough that some relearning is needed (I often try to do stuff the Illustrator way, because that's what I've gotten used to through nearly 20 years, and the application does something completely different).

Scribus, page layout, multiplatform.
I... still haven't managed to make heads or tails out of this one, but I intend to. Again, I'm used to InDesign (though I haven't used it for nearly as long as Photoshop and Illustrator, it's similar enough to the other Adobe applications that the familiarity has quickly dug deep paths that are not all too easy to get out of).

Much of your skills learned from those courses will be quite specific to the Adobe applications, and the interfaces are very different (with the exception of Paint.NET, but it's more lightweight and not quite as powerful).

Reasons for me switching? There's two of them:
1. Adobe don't make their application for Linux (Wine works, to some extent), and I switched away from Windows a few months ago.
2. I don't agree with the idea of subscribing to Creative Cloud (and unless I accept the cloud, I won't be able to upgrade beyond Creative Suite 6).

Gimp has a plugin that gives it the "Look&Feel" of photoshop.

Inkscape is more similar to the old Adobe Pagemaker than to InDesign.

Just to add to the already mentioned list: Blender - a 3D software that may be useful to do some renders.