Hyperspace

General Description

Intro

Hyperspace is a mysterious dimensional plane that allows humans (and other races) to travel with faster than light speed, being the one and only thing that makes creating interstellar empires possible. The word 'mysterious' isn't used without a reason, since even despite using it for hundreds of years, there exist not a single theory that explains how exactly it is working. With Hyperspace Drive not fitting into any scientific theory to ever exist.
What remains, are speculations and conspiracy theories. Further fulled by extreme rate of suicides and insanity among hyperspatial physicists. Which can be considered a sort of tradition of hyperspace, dating back to mankind's first flight in hyperspace, with all people on a Discovery returning slightly... different.
What allows it to be use as a method of bypassing the restriction of a light speed is that it's space is 'compressed' when compared to one in the Realspace. 1ly in Hyperspace is an equivalent of 1,5 to 500 ly, with compression rate of 70-200 making up for 95% of space. Because of that, a ship has to travel through only a fraction of the actual distance of travel.

Travelling through Hyperspace

Entering Hyperspace

Safe entry to the Hyperspace is typically possible only on the verge of the star systems, however the exact distance from the local star varies depending on the star type and size (it's believed that the entry zone size depends on the strength of gravity fields in the area, though it's not known why or how). In case of the Solar System, the safe zone starts slightly behind the orbit of Pluto and ends near the outer edge of the Kuiper's Belt. Entering Hyperspace within the star systems means certain death, while doing it outside the entry zone seems to destroy ships at random.
It is unknown why exactly the exit or entry beyond that border is so dangerous, which results in outlandish theories about the 'Terminus Beasts', some terrifying space beasts inhabiting the void between stars, who are the reason for the destruction of ships (at least those with the distinct bad luck of trying to exit the Hyperspace only to land right next to one). Or perhaps some terrifying and eldritch alien species that lives in he cold space away from light. Myths are numerous.

Observing Hyperspace

Even describing hyperspace is a problem, for a simple reason. Hyperspace itself is an extremely potent cognitohazard. Seeing or hearing it shatters minds of every observer, regardless of whether it's sapient or not, synthetic or organic - the results are either going completely insane or dying, or dying after a while of being completely insane. Even employing computer analysis tends to cause cascade of error that can destroy the computers employed - which is why visual sensors are useless in Hyperspace (and why there are no hyperspace sonars despite the fluidity of the medium making such a technology into something which could work).
The result is that people operating outside of a warship while in the Hyperspace (typically boarding parties) are forced to rely on touch and highly imperfect wave sensors - there are natural 'waves' (typically nothing more but small 'ripples') going through it, which bounce off all surfaces. Running a perpetual computer analysis of such 'ripples' allows people out there to be roughly aware of the shape of their surroundings, but it's far from being able to see. This technology is slightly more detailed when the Hyperspace is peturbed, as this means more of waves, that are also slightly more 'detailed' themselves.
Worst, the Hyperspace doesn't even have to been observed directly to start causing insanity. Simply staying (even in perfect isolation) in Hyperspace for longer than two weeks is going to cause a negative effect of sanity of all living (or synthetic) entities. The symptoms typically resemble a rapidly intensifying paranoid schizophrenia, though there are also cases of much different sets of symptoms. After twenty-five days there's typically no one left to save aboard drifting wrecks.

Hyperspace Medium

The Hyperspace seems to be a liquid in form, though a liquid most peculiar. Humans in a spacesuit can swim in it simply by waving their hands and legs around. Artillery can shoot, but its range is attrocious (counted in dozens of kilometers rather than around one million), and missiles and starfighters are simply no good (resulting in Hyperspace-adapted shuttles that are closer in construction to submarines). The hyperspace medium is also capable of dispersing energy weapons, their range shortened about as much as the MAW artillery.
Curiously enough, the thermal 'dispersion' of such weaponry is massively limited - the laser ray seems to barely increase temperature of the surrounding hyperspace medium. As a result, the weaponry overheats faster than in Realspace, but not as quickly as it should when submerged in a liquid. The rays and plasma dissipates much faster than they should, regardless of limited heat dispersion through an unknown mechanism (leaving a 'line' of peturbed medium, 'dispersing' the absorbed energy in the form of waves).
The larger the object, however, the lesser the friction. Even a frigate is enjoying a frictionless environment, despite flying through what is de facto water. What's more, the sufficiently large ships (typically capital ships and largest cargo vessels) actually suffer from (slight) 'negative friction', accelerating faster than they should have (which is typically used to save some of the valuable fuel, though if ships lost their means of decceleration things might get ugly).
Attempts to analyze the liquid material that fills the Hyperspace ended up with failure. It doesn't drive anyone insane (though it will cause hallucinations in observers, and might cause mental problems when one gazes too much at it), but all machines used to analyze its components with bring back nonsensical results (the same bottle of hyperspace 'liquid' might be made of liquid lead, human blood, primordial soup or sea water in subsequent tests, with not changes to its texture or properties).

Hyperspace Pressure

Generally the higher the spatial pressure the faster the travel, however sufficiently large pressure will cause ships of less resistant construction to suffer damages (and is generally described as 'unpleasant' to the crew). An extreme level of spatial compression might destroy ships and kill the crew. The only reason why the travel through Hyperspace is possible (despite the 70x compression rate being considered average) is because large objects being generally resistant to the compression - what is 70x spatial compression will be 1,050x compression for a ship.
Smaller objects (such as humans attempting boarding operation) generally have a set ammount of time (which depends on their mass, velocity and density) before the pressure they are subject to starts growing from the level of the ship they just left. The growth is exponential (though to a set upper level where the pressure starts being constant), meaning that it starts slowly but then begins rapidly accelerate. First negative effects begin manifesting after about 56 minutes of exposure, with death happening after around 67 minutes.
Hyperspace is also spatially unstable. Being more compressed than Realspace is what allows it to be used as a medium for FTL travel - however its all but stable compression. Parts of this realm grow and shrink almost permanently and with no clear patterns to that changes. While changes are typically gradual, there are cases of powerful compression changes damaging or even outright destroying ships. Such an incoming 'pressure waves' (as they are nicknamed) can typically be predicted due to certain patterns of activity in the Hyperspace (typically relatively stable decrease or rise in pressure, often described as a 'build-up' before the energy is discharged as a pressure wave).
This gives the ship time to react, typically by reaching the safe harbour before the discharge occurs. With the build-up typically lasting for days, this is possible. If not, emergency exit from the Hyperspace is seen as the only way of saving a ship (though it's a dangerous thing for the crew, so its' always a last-case scenario).

Hyperspace Navigation

The stability issue also seems to affect the distances and directions. The straight line between two relatively close star systems in the Realspace will not be straight in the Hyperspace. It might bend and twist a lot. The only thing that can be detected from the Hyperspace is the star system as a whole (mostly due to general 'bumpiness' of a flight, as the gravity field of the objects seem to influence the ship, causing it to jerk around).
The result of one of the earliest scientific breakthroughs were the patterned hyperspace wave generators, a sort of a radio transmitter that could be placed in the Realspace while projecting a signal going through the Hyperspace. While initially created with hope that it would become a form of FTL communication, it ended up as a navigational beacon. They are placed in the exit zones, showing where it's safe to exit or enter the system. There are also occasionally dropped (in the more stable areas) in the void between stars, used to as a navigational assistance for a travel between two star systems (they have a hyperspace drive installed and are automatically dropped there 'from' the Hyperspace).
The problems are also regular waves going (in three dimensions) through the Hyperspace, which in case of really strong ones can push ships off course or even throw it around, potentially causing symptoms similar to seasickness. And sometimes there are the hyperspace storm - a prolonged and mobile areas of distortions that generate powerful waves coming and going in random directions. If they strike, seasickness is the least horrible thing that can happen to a ship.