For you ...
As a citizen of a Member State of the European Union, you have the
right to enter any other EU country without having to comply with special
formalities. All you need is a valid passport or identity card.
Your right to travel may be restricted only for reasons of public
order, public security or public health.
Accordingly, your right to travel does not depend on your situation;
whether you are traveling for professional or private reasons, whether
you are working in an employed or self-employed capacity or whether you
are simply a tourist, you have the right to travel anywhere in the Union.
Provided your stay in another EU Member State does not exceed three
months you do not have to ask for a residence permit. The only constraint
that may lawfully be imposed on you in certain countries is a requirement
to notify the authorities of your presence. In most cases this is done
automatically when you check in at the hotel or when your landlord fills
in a declaration in respect of the tenancy.
If you stay for more than three months you must apply for a residence
permit.
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...and members of your family
Members of your family, whatever their nationality, may go with you.
Your family is defined as your spouse, children under 21 (or dependent on
you), as well as your parents and your spouse’s parents, if they are also
dependent on you.
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...who travel with you
Members of your family who are traveling with you should, as a general
rule, also have a valid passport or identity card. The legislation of the
Member States often provides, in the case of minors, who are not
personally entitled to such a document, for the issuance of a special
identity card or for an entry to be made in the passport of one of the
parents.
Please note that, if members of your family are not EU nationals, the
Member State(s) to or through which you intend to travel, may, depending
on the nationality of the individuals concerned, require an entry visa. This visa should be
granted free of charge and without undue formalities by the relevant
consular authorities.
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...who travel alone
Caution, however: the right of travel enjoyed by the members of your
family under Community law is not an independent right, in other words it
applies to them only if they accompany you. Accordingly, members of your
family who are not nationals of a Member State of the European Union are
not entitled to the visa arrangements mentioned above when traveling
alone.
On the other hand, members of your family who are not nationals of a
Member State of the European Union do not require an entry visa if they
reside in an EU country that has signed the Schengen Agreement and wish to
travel to another Schengen country: they may travel freely and without a
visa in the Schengen Area provided they are in possession of their
identity document and their residence permit.
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source: European Commission