OK, I don’t know what you can get where you are.  However, you could start with the “golden age” authors:  Isaac Asimov, Arthur Clark and Robert Heinlien.  Any of their works are going to be good.

For Asimov and Heinlien, you may want to do some research first because a fair bit of both author’s works are tied to a series chronology.  A couple of titles that are not:

Asimov:  The Gods Themselves

Heinlien:  Stranger In a Strange Land

For Clarke, try Childhood’s End.  Also, see if you can dig up a collection of short stories with a copy of The Sentinel (that was an early version of what became 2001).

Past that, keep an eye out for Larry Niven.  Especially the Ring World series and the Integral Trees books.

You may also want to keep an eye out for C. S. Friedman’s True Night series and Julian May’s Galactic Milieu series.

Iain M Banks, well-plotted, fantastic but convincing, well worked out settings, fast-paced often complex plots. 

Most recent SF novel is "Matter". Right up to his standard.

Stephen Baxter. Actually co-wrote "Time's Eye" with Arthur C Clarke, published in 2004.

Peter F Hamilton - definitely hard SF, with some weird elements, at times.

There are more, but those name dominate my most recent pile, at least in SF - I'm also into some Fantasy authors as well...

Not me. Not familiar off hand.

I almost mentioned Orson Scott Card. The Ender series really worked for me.

My super favorite fantasy author is Stephen Donaldson. The Tales of Thomas Covenant, the Unbeliever. Into its Third trilogy. Absolutely fantastic, with the sort of edge that should appeal to a hard SF enthusiast.

I liked Terry Goodkind's 'Sword of Truth' series.

I don't know how much known fact that is, but Frank Herbert didn't write just Dune. He wrote many books from the times before and after Dune. Some of them are post-mortem, finished by his children from numerous and complex notes that were found in some safe, somewhere. I've read most of them, and I have to say, though the premise is desperately unoriginal (humans vs evul robotz) everything else is a masterpiece.
They are all translated to Czech language. I don't know if you can find them in common bookstores in Slovakia. I personally like to visit an e-book collection, belonging to a certain Rob'em Good of Sharebook forest.

basically sci-fi about the future of mankind--as opposed to made-up systems like in star wars or dune--with more or less scientifically plausible situations.

"Tau Zero" by Poul Anderson is a pretty good example of hard sci-fi. It starts off a little dry but is a pretty good book once the story starts moving about 30 or 40 pages into the book.  Joe Haldeman is one of my favorite sci-fi authors and the aforementioned Orson Scott Card writes some pretty good books, particulary the first book in the "Ender's Game" series (the rest sucked after the first book, in my opinion).

If that's what you're going by, I'll recommend "The Book Of Dave" again, by Will Self. Although it's more of a post-apocalyptic kind of a thing, I guess. 

Anything by Iain Banks is indeed worth reading.

As for Orson Scott Card, I do believe he sucks wet farts out of dead pigeons, but that's just my opinion.

That is a fair question. For me, I don't think that there is a clear line where one can apply a binary choice. Lots of stuff can be hard sci-fi without being grounded in immediately predictable technology.

Sure, there are entries that are pretty clearly grounded in what we can do in the near future if we are willing to do so. Asimov's “Marooned off Vesta” comes to mind as an example.

However, I would still consider a work to be firmly in the sci-fi field if the author choose to introduce elements of possible technology and then explore what comes from such things existing. To me, it matters little if those things ever come to be provided that there is some reasonable exploration of the effect of such things in general.

Sci-fi that tries to ground itself in real science rather than going off onto fanstasy-woo type stuff. Star Wars and Dune are extremely 'soft' on this scale. "Hard" sci-fi tends to deal with what it would actually be like to try to be a space traveling species. Ie: taking thousands of years to travel from one star to another, not having psychic or mystical powers, and no turning on a magical device that allows for faster than light speed travel.

"Dune" was a masterpiece. It was one of the softest sci-fi novels ever written, but I think it is one of the best novels ever written. God Emporer was also an amazing book. The other books written by Frank Herbert were of lower quality (not as amazing as "Dune" ), but still rather good novels. The "Dosadi Experiment" and the "Jesus Incident" were good. "Hellstrom's Hive" was very poorly written, but had great sci-fi concepts in it. The books written by Frank's son and that other author are pure shit. I don't believe for a second that they are based off of Frank's notes. They contradict Dune cannon constantly. They contradict "Dune" cannon so much that they simply can not be in the same fictional universe as the origional "Dune" series. It pains me that Brian Herbert is raping his father's legacy in order to churn out those pulp novels. I don't mean to go into a fanboy rant against Brian Herbert, but "rape" is the only word that can used to describe what he is doing to his father's life work.

"I think the difference is the same as between Star wars and Star Trek. Star Wars don't include an intriguing episodes of how the lightsabers were invented, how midichlorians were discovered, or how Chewbaccas were finally proven to be intelligent species "

Actually, Star Wars has covered all these things. Lightsabers started as crystal swords. Chewbacca was a Wookie, from the planet Kashyyyk. Medichlorians are mitochondria with a cool ability.

I would say both Star Trek and Star Wars don't qualify as hard sci-fi. Both lean heavy on the mythological, and both are in created settings. Star Trek might use our actual galaxy as a starting point instead of making a galaxy up, but they built so much on top of it that there's no real difference between them. You have the Force in one, Q in another, and both depend on a FTL speed which has largely been proved as impossible.

Stargate is closer to good, hard, sci-fi.

A couple of my favorite SF authors who might suit your interest are Harry Harrison and Crawford Killian.

By Harrison, check out "Make Room! Make Room!". The film "Soylent Green" was based on this book, though I think the book is much better. Also, try his "Eden" trilogy - "West of Eden", "Winter in Eden" and "Return to Eden" - which is based on the "what-if" scenario that dinosaurs never went extinct, and they developed societies, weapons, etc. alongside humans. Lastly, you can also try "A Rebel in Time", about a modern-day U.S. Army colonel who smuggles weapons technology back in time to help the South win the Civil War and the black sergeant who is sent back to stop him.

By Killian, I would recommend his "Chronoplane Wars" trilogy - "The Fall of the Republic", "Rogue Emperor" and "The Empire of Time". Basic summary is that humans develop the capability to travel into the past and manipulate events without actually changing the timeline, and there is a CIA-type organization in charge of it all.

at the risk of sounding like both a necrophiliac and a pedophile, i admit it: i've always found that picture of the zombie little girl extremely hot.

is it necrophilia if it's a zombie?  and do statutory rape laws apply to zombies?

this is hard sc-fi, btw.

oh come on, man, the original films were basically good vs. evil king arthur myth warmed over with lasers.  as for the prequels, if you don't think those were monumentally childish, then obviously we work on two different astral planes.  it's a pity, too, because the prequels had much more potential for complex ambiguities than the original films, what with the anakin-->vader transformation.  but they just plain fucked it up.

yes, nobody is arguing that star trek isn't the softest of the soft--in fact, their campiness is part of their appeal to me--however, as i said, they regularly address the existential problems of humanity.  quite frankly, i like it that aliens are on the periphery.  i mean, star wars swings way too far in the other direction.  what the fuck are humans in star wars?  where do they come from?  who gives a shit?  like i said, they're there so the normal film-going slob can identify with the protagonists.  also, let's not forget the fact, as was hammered to death in another thread about a year ago, that star wars rips a great deal of its shit off dune.

still, i should make it clear that there are only two parts of the star trek mythology that interest me: the films and TNG.  the original series is just bad.  sorry, i really think so.  the films (at least up to generations) are incredible, especially, imo (and this isn't a common choice), the first one.  i just find the idea of v'ger to be really fucking awesome.  as for TNG, that series was golden.  the borg rock and star wars has NOTHING that original (first contact and voyager fucked up the borg, which is why i ignore both).  also, you can't say that TNG didn't try REALLY hard to explore alien psychologies.  the klingons are much more developed than in the original series, and the whole vulcan/romulan dichotomy is great.  of course star trek aliens are much more humanoid than star wars aliens, for the simple reason that the producers of star trek never had the kind of resources that industrial light and magic has (and it's a pity, because lucas pisses them away).

i don't make my choice between star wars and star trek based on which is "more grounded in reality."  i think it's been pretty well established in this thread that any sci-fi which uses a sort of "hyperspace" or "warp speed" as a plot device has forfeited any claim to hardness.

"oh come on, man, the original films were basically good vs. evil king arthur myth warmed over with lasers."

And the first Star Trek was nothing more than morality tales too. There was no science at all in the series back then, beyond use of technology.

"as for the prequels, if you don't think thosewere monumentallychildish, then obviously we work on two different astral planes.  it's a pity, too, because the prequels had much more potential for complex ambiguities than the original films, what with the anakin-->vader transformation.  but they just plain fucked it up."

The only thing childish and fucked up about the prequels was Jar Jar. Everything else was brilliant.

"i mean, star wars swings way too far in the other direction.  what the fuck are humans in star wars?  where do they come from?  who gives a shit?"

Just another species, the way it should be. Star Trek elevates humanity above and beyond all other life. It elevates us even beyond an actual god, Q. In Star Wars, we're just another species.

(made possible by Star Wars, ironically), with 60 minutes of storyline that made Voyager into a super weapon. Add a hot bald chick and a command dilemma and you've got a film I'll never watch again. The potential was there, but nothing happened.

" the borg rock and star wars has NOTHING that original (first contact and voyager fucked up the borg, which is why i ignore both)."

I would argue that was ST ripping off Doctor Who. It wasn't really original. Though the Borg are the epitome of awesome. But Species 8472 doesn't hold a candle to the Yuzzhan Vong.

"also, you can't say that TNG didn't try REALLY hard to explore alien psychologies."

I can. Every single alien problem is based on a human one. Many of which were current events of the time. Beyond current events, Klingons are just Spartans with space ships. The Vulcan/Romulan rift is mirrored by plenty of real life scenarios, most closely the American split from Britain. And multiple church splits before that.

Trek is clean and shiny, Wars is dirty and gritty. Trek examines ourselves, Wars makes us think about other possibilities. Wars uses military convention and strategy, Trek makes things up as it goes along.

Most importantly, for a story, Wars has a 30,000 odd year old history with unprecedented continuity. Literally unprecedented. Trek rarely keeps continuity through a season, let alone its entirety. Not one book is cannon. And its timeline is no more than 400 years. Worse, every year that goes by, Trek loses continuity simply by tying in to reality. Wars never crippled itself that way.

So I love both, but love Wars a lot more.

Does 1/2 Prince count?

from wiki:

1/2 Prince (1/2 王子, 1/2 Ouji, Half Prince) is a Taiwanese manhua by Yu Wo and illustrated by Choi Hong Chong. The story takes place in the year 2100 A.D. where humans have developed highly realistic virtual reality games. The protagonist, 19 year-old female college student Feng Lan, is challenged by her twin brother Feng Yang Ming to play the newest popular virtual reality game - Second Life - without using the advantages of being a female character in the game. She decides to play as a male character and prove her skills as a swordsman.

So basically:

In the future almost everyone is playing virtual reality MMOs as hobbies. Some people have bad addiction to it and will skip work/school to play. 

JJ Savarin - Lemmus I, II, III

C. S. Friedman - Coldfire Trilogy

And as an aside and nothing to do with 'prediction' Sci-Fi.

All of the Discworld novels by Terry Pratchett.

My already high opinion of you has just increased.

Sausage in a bun, sir?

 I have all the Pratchett discworld stuff as well. Entertaining reads

Oh, if you like those I'd suggest "Kingdom for Sale".

None of these are "hard sci fi" though. Still, good fantasy.

Clarke is good...I've read some of Asimov's short stories, but Frank Herbert's Dune series IMHO is probably the greatest sci-fi ever written.