Welcome to the forum Grandur!
A lot of tree climbers climb by ascending ropes and then setting the rope higher up and climbing the rope again and so on.
It sounds like you want to actually climb the tree itself, which is the way I like to do it. However I agree with Oldtimer: always have a harness and a rope over a branch above you as a safety backup.
There is a lot to explain so the idea of going to an arborist to learn and reading the information on this site is essential and you will learn lots of ways to make the whole thing much easier.
Things to consider are:
How to check that the tree and the branches you are using are safe
what is the best type of rope and other gear
the knots that come in handy for every situation
how to get the rope over a branch high up
how to use a friction saver to protect the tree from rope burns
how to climb the rope to the branches and abseil back down
how to ensure you are always attached to at least one strong branch while you are climbing
how to ensure that there is never any slack in your ropes so that if you did fall there would be no shock load on the branch you are attached to
how to ensure that you always can abseil back to the ground if you got stuck or injured
It sounds like a lot of things but arborists and the experienced recreational climbers here have developed the easiest and smoothest ways of doing everything and it's all here for anyone who wants to know!
I also bought a copy of The Treeclimber's Companion by Jeff Jepson when I was learning. It's only a short booklet but has lots of information packed into it.
Good luck and let us know how you get on!
Take care,
Michael