Form I-131: Application for Travel Document is used to apply for the following types of travel documents.
1.
Reentry Permit - A reentry permit allows a permanent resident or conditional resident to apply for admission to the United States upon return from abroad during the permit's validity, without having to obtain a returning resident visa from a U.S. embassy or consulate.
2.
Refugee Travel Document - A refugee travel document is issued to a person classified as a refugee or asylee, or to a permanent resident who obtained such status as a result of being a refugee or asylee in the United States. Persons who hold such status must have a refugee travel document to return to the United States after temporary travel abroad unless he or she is in possession of a valid advance parole document. A refugee travel document is issued by USCIS to implement Article 28 of the United Nations Convention of July 28, 1951.
The document may be accepted by a transportation company in lieu of a visa as an authorization for the holder to travel
to the United States. An advance parole document is not issued to serve in place of any required passport.
3. Advance Parole Document - An advance parole document is issued solely to authorize the temporary parole of a person into the United States.
Official Link to Form I-131 Instructions
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From U.S. Customs & Border Protection.
What documents, identification, paperwork does a U.S. citizen or legal permanent resident (LPR) need to travel internationally?