sole trader business
The simplest way to run a business in Sweden: you and the business are the same legal person, so you are personally responsible for its debts, and its profit is taxed as your income.
To register as a sole trader you must be over 16 and have a Swedish personnummer or coordination number, and you must not be bankrupt or banned from running a business. You apply for F-tax, and VAT and employer registration if needed, through verksamt.se.
Many newcomers start a sole trader business for freelance work. If you hold a work permit, check with Migrationsverket first, since a work permit is tied to employment.