The Form I-131 is needed when you wish to leave the United States and return again. It is for a reentry permit, refugee travel document or advance parole travel document, to include parole into the U.S. for humanitarian reasons.
The Form I-129F is used for a number of purposes. It is used to petition to bring your fiancee (K1 Visa) and that person’s children to the U.S. for marriage to you amongst other applications. You search this website for more information.
The Form I-134 is used to show that visa applicants have sponsorship and will not become public charges while in the United States. The sponsor must file a separate affidavit for each applicant.
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The Form I-765 allows you to work in the United States. You need to file this application before you start employment in the US. Speak to US Immigration Services about what needs to be filed with this.