"Without a notary? That can't be safe." The reaction is understandable, but it rests on a misunderstanding. Sweden needs no notary because the legal system handles the purchase differently, and just as bindingly.
Why no notary?
The notary is a feature of the German legal system, and of a few others. Sweden simply never needed one for a property purchase. Instead the process is set out clearly in law (Jordabalken). It is no loophole and no grey area, but the normal route prescribed by law, the one every Swede follows in exactly the same way.
The four steps
1. Köpekontrakt: the purchase contract
A written contract between buyer and seller. It states the property, the price, the conditions and the signatures of both sides. With that, the purchase is legally agreed.
2. The payment
The purchase price is paid, by bank transfer, with a clear record. In a rent-to-own arrangement the payment runs in agreed instalments (see Financing & rent-to-own).
3. Köpebrev: the deed of ownership
After full payment, the seller issues the köpebrev. It is the receipt and the formal proof of ownership. It confirms that the purchase is complete.
4. Lagfart: the registration
With the köpebrev you apply to the land survey authority (Lantmäteriet) for the Lagfart: the public registration that the property now belongs to you. There is a deadline of three months from the purchase. Only the Lagfart makes your ownership publicly visible, comparable to a land register entry.
Witnesses instead of a notary
It is usual and sensible for the signatures to be confirmed by witnesses. This replaces the function a notary carries out elsewhere: a clear, provable conclusion of the contract. The difference is the form, not the security.
The one thing you need to watch
Don't miss the Lagfart deadline. And make sure the köpebrev only changes hands after full payment. That is part of a clean process. The exact process at Rabenfels is set out step by step on the How a purchase works page.