This
www.osh.dol.govt.nz/order/catalogue/pdf/treefell.pdf and this
www.osh.govt.nz/order/catalogue/pdf/chainsaw2.pdf
are both very good reads (I can't currently connect but nopt sure if that's me or the links so give them a go) - intended to help safety wise by the NZ government as there are large numbers of agricultural and home users who just aren't going to attend an NPTC or equivalent course, probably just like many agricultural and garden users in the UK and no doubt Sweden too.
A few things to bear in mind - chainsaw safety is one thing, such as a proper awareness of maintenance and actually doing it. Wear protective clothing, helmet and visor etc. Knowing the safe ways to start the saw, and stances, and how to move with the saw are all crucial, no matter what you intend doing with it. Learn well, and follow the correct procedures every time, make it a real habit and don't rush, get lazy or work in poor light or cramped surroundings.
All this is fine if all you're doing is basic crosscutting of straight timber - I have done this regularly after basic learning, albeit with a very experienced arboriculturalist, but I am not 'trained and qualified'. This is not to say that I don't advocate proper training, just an acknowledgement of the fact that not everyone will take it on.
The thing that may be a worry Abbe, is that you may want to use a chainsaw to fell trees in the forest, or to dismantle fallen trees. Both operations carry inherent dangers that you don't need to get wrong to learn the mistakes from, as they may be your last mistake.
Felling standing trees in dense forest can lead to 'hung' trees, unsupported at the base and unstable in the canopy.
Likewise fallen trees are supported by branches, and potentially cutting only one branch can end with the entire stem lashing out, twisting and falling in just the wrong direction.
I think that if you can get the certificates, and can afford the time and money, get them (why not), and even then it's worth practising with an experienced forester / user until you know what you're doing. Otherwise I wouldn't rule out just learning with the experienced guy if you can, as it will work out (and that's once how everyone did it after all) Even better is to never use a chainsaw alone, especially not in the deep woods. It wouldn't do to have contact between chain and leg, and no-one to help.
Hope that helps...