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You need to use an outer join, otherwise you won't get those students back that did not borrow a book.

Then you need to count() on the students table, not "the group" (which is done when you use (*))

SELECT
    LEERLINGEN.LLNR,
    LEERLINGEN.VOORNAAM,
    LEERLINGEN.TUSSENVOEGSEL,
    LEERLINGEN.ACHTERNAAM,
    LEERLINGEN.KLAS,
    COUNT(LEERLINGEN.LLNR) AS AANTAL
FROM
    UITLENINGEN
    LEFT OUTER JOIN LEERLINGEN ON UITLENINGEN.LLNR = LEERLINGEN.LLNR
GROUP BY
    LEERLINGEN.LLNR,
    LEERLINGEN.VOORNAAM,
    LEERLINGEN.TUSSENVOEGSEL,
    LEERLINGEN.ACHTERNAAM,
    LEERLINGEN.KLAS
HAVING
    COUNT(LEERLINGEN.LLNR) = 0;

I dont' know MS-Access, but I assume it supports outer joins using standard SQL.

user1822