I think his fur is tangled..?

I've never felt how a cats fur feels like when it has gotten tangled, so I'm not sure if this is it, but I think so.

Under his arms, a bit on his stomach and around his groin, there are these lumps. They feel just like his skin, and they look like flat clumps of hair. They don't feel like something I can comb out, and I certainly can't cut them out, because I probably won't feel where his skin begins.. 

What is it, and what do I do? 

Sounds like typical mats, common especially in spring as they shed out their undercoats.  If you are not experienced, you are correct not to attempt to remove them with scissors.  The best thing to do is take him to an experienced groomer (or use the kind that comes to you) and have the mats shaved off with clippers, or you could even get him a Lion Cut, which shaves the whole body but leaves mane and tail tip.  .He should also get a bath to remove excess oil that is making him mat.  The hair then becomes silky and doesn't cling to other hairs and the cats don't mat for awhile.  Whenever they start getting bad tangles, it's time for another bath.

I didn't even realize there were cat groomers...

Do you think a dog groomer is experienced with cats as well?

I've seen these "furminator desheddind" things in the store, do these work? 

When I give him a bath, should I use cat shampoo? I usually bring him with me in the shower, because then he doesn't fight me, this is okay, right?

Sorry for all the questions, and thank you for your answer! 

Bringing him in the shower with you for HIS bath is not a good idea.  Most groomers are experienced with cats and dogs, and some specialize in cats.  There should be many articles out there, including videos, but starting with a groomer would probably be your best bet for the first time.  BTW step ONE should be clipping all 18 nails.  Here is my greatly edited SHORT version of  basics on how to bathe a cat:

Best to do at a kitchen sink with counter next to it. Do NOT put water in the sink and do NOT put cat into sink. Put cat on counter on dry towel. Have container of warm water at hand but do NOT pour it on cat. Put shampoo on cat’s neck in a ring to start (in case of fleas, they cannot get to head and eyes through the soap), massage shampoo into neck and keep adding small amounts of warm water to make suds. Most cats like the neck massage even if it’s a little wet. Continue working down the cat towards the rear. Once majority of the cat is wet, you can usually put his hind end in the sink, use the spray to rinse, by keeping it right against his body. Squeeze out excess water with your hands and alow him to walk back up on counter. Wrap him in that towel and then another outside of that and hold to blot dry for awhile. Depending on the cat, you can then gently comb dry in front of hair dryer set on low, one part at a time (the rest remains wrapped in towel).  Otherwise, towel dry as best you can and then put in a small room that you can heat up very toasty until he is dry.

Furminators work for helping to remove the undercoat during shedding time but they do not work for removing mats.  They would just pull and hurt the cat.  There are wide tooth metal combs that have a curved blade on one end that is good for cutting mats before then combing them out, but if they are already at the skin and pulling, shaving is really the best method.

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His claws are kept short

This is probably a stupid question, but why can't I bring him in the shower? He doesn't attack me when I do it, and don't even get mad at me afterwards, he even licks me clean   

I didn't say you couldn't bring him in the shower with you for fun, when YOU bathe, but for HIS bath, it needs to be all about HIM, getting him thoroughly soaped and very thoroughly rinsed because any soap left in his coat can be an irritant.  You can do this much better when you have your clothes on, both hands free, and are not  in danger of dropping the soap.  Trust me.

Do NOT bathe a cat or rinse it with the slightest bit of mats as it will get worse! 

Yes, the bath suggestion was for AFTER the mats have been removed!

Red Top Rescue said:

 
I didn't say you couldn't bring him in the shower with you for fun, when YOU bathe, but for HIS bath, it needs to be all about HIM, getting him thoroughly soaped and very thoroughly rinsed because any soap left in his coat can be an irritant.  You can do this much better when you have your clothes on, both hands free, and are not  in danger of dropping the soap.  Trust me.

Click to expand...

What if I bring him into the shower without showering myself? Just focusing on him? If not, I'll try the sink (if my mom don't freak out), after the mats are removed. Sorry, I just have no knowledge on this matter..  

But I guess for now I just have to get hold of a groomer

Many dog groomers don't groom cats. Some don't like cats or are scared of cats. It's a different skill. I would look for a cat groomer -- someone who specializes in cats, or a pet groomers who has "cat-only" days at their salon. 

It's safer not to try to cut the mats out yourself. Cat skin is thinner than dog skin. It is surprisingly easy to nick the skin, especially under the arms and on the belly. Cats usually won't react when you nick them, so you won't know until later on that you have cut your cat. A small cut can widen into a bigger gash when the cat moves around.

I shower with my cat. She's very relaxed in general. 

withoutaname said:

 
What if I bring him into the shower without showering myself? Just focusing on him? If not, I'll try the sink (if my mom don't freak out), after the mats are removed. Sorry, I just have no knowledge on this matter..

 

But I guess for now I just have to get hold of a groomer

Click to expand...

The shower puts water on top of the hair coat, while the sink sprayer attachment can rinse right against the skin and get all the soap out.  Just get the groomer to bathe the cat after getting the mats out, then you won't have to worry about it.

Red Top Rescue said:

 
The shower puts water on top of the hair coat, while the sink sprayer attachment can rinse right against the skin and get all the soap out.  Just get the groomer to bathe the cat after getting the mats out, then you won't have to worry about it.

Click to expand...

Yep, I think it's definitely a good idea to get the groomer to do it, because you lost me at sink sprayer..

Now it's just the even more difficult task that remains: finding a cat groomer!

Will it make much of a difference if I postpone bringing him to the groomer to late next week?

Postponing until next week should not be a problem.  The mats might get a little bigger but they are coming off anyhow so should not get big enough or tight enough to damage his skin yet.  That IS what would happen if you let them go for a long time, however.  As for finding a cat groomer, you have not added where you live to your profile yet, but many vets have groomers that come in once a week or so, or they can refer you to a groomer.  Also, the large pet store chains also have grooming salons (Petco and Petsmart for instance.)  and many have at least one groomer who is experienced with cats.  If you are not near either of those stores, try Googling Cat Groomer or Cat Grooming and see what you come up with.

It seems as if the closest cat groomer is around 500 km away, but I've been asking around so maybe I'll find someone. 

It seems as if a majority of the vets here does offer help with mats though, so if I can't find I groomer, I might get help there 

The vet offices certainly do have clippers and the ability to shave off the mats without cutting the cat.  They may also be able to refer you to a cat groomer.  Since you use the term "km" instead of miles, I gather you are not in the U.S.  We are an international site, however, so if you tell us where you do live, I'm sure some of the members in your country may have some other suggestions.

We live in Norway  

I'll call one of the clinics as soon as I can! Hopefully, this time next week he'll find himself without any mats