The companies register (Swedish: aktiebolagsregistret, sometimes aktiebolagsregister) is the register in which Bolagsverket records details about every Swedish limited company. It shows, among other things, the company name, company registration number, share capital, board and articles of association.
The companies register does not show who owns the shares. That information is kept in the company's share ledger, which the board itself is responsible for. The two complement each other, and both are needed for a correct picture of the company.

Bolagsverket is the Swedish authority that registers companies and company information.
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A share ledger is a record of a company's shares and who its shareholders are.
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A company registration number is a unique identifier for a company or association.
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Share capital is the capital the shareholders contribute to a company in exchange for shares.
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